There's a number of threads on better quality plastic sets already, why don't you just look at those.
I scanned through some of the pages of this thread https://www.chess.com/forum/view/chess-equipment/post-your-favorite-plastic-chess-setsnot-for-snobists
But, it doesn't say if plastic pieces can be soaked in water.
Taking your last consideration first, the latest scientific evidence is that the Corona virus does not stay active for very long at all on surfaces. Studies were done and they found that even in a room with a person having the virus active and being contagious, the surfaces in that room only had the non-contagious remnants of the virus. The virus itself is very fragile and cannot survive very long at all on surfaces.
It then depends on what type of playing situation you plan on using the set for. If you plan on using it at home, constant cleaning would not be called for.
If you plan on using the set in either an over the board club or tournament setting and the virus is still active in your area, then sanitizing the pieces would be quite acceptable.
To sanitize or clean the pieces from any possible contagious virus, I think washing the pieces under running water with soap is too much.
There are a number of disinfectant sprays currently available that will kill the contagiousness of the virus and still not cause damage to the surface of a Chess piece. Yes, in my opinion using plastic pieces would be preferable. However the bottom felting should not be a concern when using a disinfectant.
There are much better places to get an appropriate plastic set other than Amazon, in my opinion. A few retail places here in the states include The Chess House, The Chess Store, Rochester Chess Center, American Chess Equipment, Wholesale Chess, The House of Staunton, Chessusa.com, to name a few.
Study suggests new coronavirus may remain on surfaces for days...
Most decent quality plastic pieces that are sold by reputable chess retailers will have felt on the bottoms. If you purchase from retailers which specialize in chess products you can contact them if in doubt. I would never wash these plastic sets in water. From my experience it's generally the least expensive, cheapest quality, toy plastic pieces which are not intended for serious play that tend not to have felt on the bottom. When soaked with water, felts may or may not fall off, depending on how well they are glued on. But upon drying I would expect that the felt would end up wrinkled and maybe shrunk, and if so, the surface of the felt would not be smooth & flat, making it very likely that the pieces would not stand stand up uniformly straight on the chess board. So I would make sure not to wet the felt.
I would recommend using hydrogen peroxide (H2O2) as a disinfectant - it kills Corona Virus (see Consumer Reports article link below). Also I purchased small 2oz. spray bottles on Amazon which I fill with the H2O2, which are easily transportable (I carry them with me when I leave home to spray my hands, face, and anything else I am concerned about). In fact you can spray the H2O2 in your mouth if you wanted (just don't drink it). It is not generally toxic to humans if used as I describe.
https://www.amazon.com/s?k=spray+bottles+2+oz&crid=37GOLZZ23LGCG&sprefix=spray+bottles+2%2Caps%2C264&ref=nb_sb_ss_ts-a-p_1_15
Caveat - be sure to get the amber-tinted spray bottles. This because light breaks down H2O2, and the amber-tinted bottle reduces/attenuates the light transmission through the bottle to the H2O2 , so it breaks down much more slowly compared to using clear glass bottles.
You could also spray H2O2 on your plastic pieces (but not the felt) to disinfect them if you like.
Here an excerpt from Consumer Reports (link to article follows)...
Hydrogen Peroxide
According to the CDC, household (3 percent) hydrogen peroxide is effective in deactivating rhinovirus, the virus that causes the common cold, within 6 to 8 minutes of exposure. Rhinovirus is more difficult to destroy than coronaviruses, so hydrogen peroxide should be able to break down the coronavirus in less time. Spray it on the surface to be cleaned, and let it sit on the surface for at least 1 minute.
As far as recommended good quality plastic sets, there are many on the market. I recently purchase the new Ultimate Chess Pieces from American Chess Equipment. @ShelbyLohrman is the owner of the site. I expect that they will last for the rest of my lifetime (under normal playing conditions!). There has been much discussion of these pieces in the Chess Books & Equipment forums over the past months - Search Ultimate Chess Pieces and Ultimate Chess Sets, etc. and look for the relevant threads.
Check the customer reviews of the Ultimate pieces here (I believe they are currently from Chess.com subscribers since the product is very new, having become available within the past month)...
https://amchesseq.com/collections/tournament-style-chess-pieces/products/bobby-fischer-ultimate-chess-pieces-with-new-and-improved-weighting-system?variant=32118482993210
other reputable online chess retailers suggested here...
Chess Sets for Club & Tournament Play...
https://www.chess.com/blog/RussBell/chess-sets-for-club-tournament-play
@Eyechess and Russbell: Thanks for taking the time to comment. I appreciate the advice and all the great links.
Why would anyone want to soak ANY chess pieces in water, unless you plan on playing underwater chess?
I don't know anything about chess set care, so I thought I'd ask the question. I was thinking maybe I could soak the plastic ones in the sink for 15 minutes, with Dawn liquid soap, the way I do with dishes. Presumably, not everyone has clean hands, so It would be nice to be able to clean the chess pieces once in a while. By the way, your tone is condescending...
Why would anyone want to soak ANY chess pieces in water, unless you plan on playing underwater chess?
I don't know anything about chess set care, so I thought I'd ask the question. I was thinking maybe I could soak the plastic ones in the sink for 15 minutes, with Dawn liquid soap, the way I do with dishes. Presumably, not everyone has clean hands, so It would be nice to be able to clean the chess pieces once in a while. By the way, your tone is condescending...
Yeah, he always sounds condescending, even when he doesn't intend to. I really don't believe it's intentional, just a "stylistic" thing. He's a good guy as far as I can tell.
"Study says this, study says that": For every study you find that says one thing you'll then find another that says the exact opposite. Every. Stinkin'. Time. Who to believe? It's December 48th, 2020, believe whatever you want! 
Back to the topic: I wouldn't expose any chess set to being washed, ever. Maybe some super-cheap, all-plastic, non-felted, non-weighted analysis set - but only if I was really, really, drunk at the time... Just wipe down the plastic pieces with a slightly damp cloth and set them in the sun for a while - the UV-C from the sun, while thankfully not intense, disinfects just fine. It's done so for a very long time!
If you're particularly concerned about transmission of something via touching a chess piece, offer gloves or hand sanitizer to your opponent. Or just have done with it and play online.
Will hydrogen peroxide hurt wood chess pieces? I ordered a travel chess set the other day, and would like to begin enjoying it as soon as it arrives, but I want to sanitize it first.
Is alcohol an appropriate sanitizer for wood chess pieces?
Since Covid-19 might be around for a long time (if it hangs around like the yearly flu), I was thinking it would be good to be able to wash the pieces in the sink with a bit of soap, but I don't know if the weighted pieces have felt that would fall off after being soaked.
If you're planning to wash the pieces, try searching for "solid" version of the standard club chess pieces. They're made out of solid plastic without weight. A number of online sellers carry them. Here's a few.
https://shop.chess.com/solid-regulation-plastic-chess-pieces-3-75-king/
Will hydrogen peroxide hurt wood chess pieces? I ordered a travel chess set the other day, and would like to begin enjoying it as soon as it arrives, but I want to sanitize it first.
Is alcohol an appropriate sanitizer for wood chess pieces?
Any insight on isopropyl alcohol as a cleaner for wood chess pieces and a wood board?
Hi PrincessJ,
Have you thought of silicone pieces ?
Hi PrincessJ,
Have you thought of silicone pieces ?
Thanks for the link! I haven't seen those before. I'll check to see if they're available in Canada. 
Hey, I found a good Canadian chess set company:
That looks like a great site - similar to HoS in some ways.
I have another question: Is a 34" x 34" folding card table too big for a chess set? Or would the tournament-type sets work well with that kind of table? I think the roll-up boards are 20"x 20" but I'm not 100% sure. I bought this table years ago, and have been using it as a craft table: https://www.canadiantire.ca/en/pdp/for-living-folding-card-table-34-in-0680429p.html#srp
I would think that size table should be fine - room for notation on one side, a drink on the other, and folded "thinking arms" in front of each player, haha! Compare yours to one of the best tables I've seen here - you're find on dimensions and hands-down winner on cost!
My only concern would be if your table is wonky/wobbly. A slight leg bump could send pieces tumbling.
@GrandPatzerDave: Oooh, that's a lovely table! My craft table is probably too wobbly. 
I owned a wooden chess set years ago, but got rid of it because I didn't have time to play at that point. Now I'm interested in buying a plastic set. I was wondering: Do all chess pieces have felt on the bottom, or only the "weighted" ones?
I've been looking for a plastic chess set on amazon.ca, but it isn't mentioned in description of the sets I looked at. The plastic sets are also either too small (especially the magnetic ones) or too big, but maybe I haven't looked hard enough...
Since Covid-19 might be around for a long time (if it hangs around like the yearly flu), I was thinking it would be good to be able to wash the pieces in the sink with a bit of soap, but I don't know if the weighted pieces have felt that would fall off after being soaked.