4" is plenty big and closer to what you see in tournaments.
What chess set size should I choose?

I wouldn't want anything over 4" Board size is a consideration. You should be able to fit 4 pawns on a square.

I'd recommend an inexpensive 3.75" set in plastic for the tournament world and then a nice set of your liking in the size you prefer for use at home.
Spend a lot on the home pieces and board then post the pictures here.
The advantage of a plastic set is that you don't have to worry about walking away from it for a few minutes at a tournament and it's also cheap enough to take to the park or coffee shop if pieces get knocked to the ground. Good for blitz too.
There are nicer plastic sets too that don't cost so much for what you get.
Here's my 3.75" HOS plastic Collector. Get black as red is non-standard for tournaments (still pretty in my eyes):
I am thinking purchasing a wooden chess from the House of Staunton.
I wanted to know what the best pieces size would be.
4'' or 4.4''?
It's not a showcase piece... as in it's not going to be sitting on a mahogany table for twenty year collecting dust.
I would like to use it in tournament play and don't want it to be big and clumsy - but also don't want it to be uncomfortably small.
Which size would fit my needs?