Best Free:
I don't know. I haven't worked hard to improve in something like 10 years. Back then it was mostly puzzles you could do online for free. These days there's probably more stuff.
Best $:
Books. But like you said, you can waste money. Read reviews, ask around, then buy 1 or 2 high quality books, and don't get any more until you've thoroughly studied them. $50 for 100 hours of instruction is hard to beat.
Also very good is chessbase. What is it? $100-200? But it's easily 100s of hours of reference material. You can use it every time you play a game, or want to work on an opening, or want to research a player, or build a collection of attacks, or endgames. There are tools to run statistics on your own games, etc.
Mediocre:
Chess coaches. I suppose they're very useful when pairing a qualified coach with a young talented player, but pairing a random titled player with an adult hobbyist? Nah. You're an adult. You can figure out how to read books on your own.
Also mediocre IMO: pretty much anything online. It's not terrible, but it's not great either.
Worst:
Books (yes I know I put them as best too)
People who buy fad books, or pretty much any book an an opening know that this is a huge waste of time and money.
I assume there is a lot of ridiculous content online too, I just haven't looked around for it.
What sort of improvement do you see?
My thoughts:
Best free:
1) YouTube videos. Especially those by St Louis Chess Club. You’ll see lots of improvement if you are a beginner. Try watching one a day.
2) Puzzle rush on chess.com. But only a little improvement seen so far. I do daily as it is easy to do and fun :D.
Worst $: Books. I saw little improvement from them once I got the basics down. I still waste about $50 a year on them in hopes of finding a good one. The only book I recommend is The Chessmaster Checklist by Andrew Soltis. So hundreds of dollars over the years for little benefit.
Best $: www.chesspractice.com. I see continuous improvement. After each game, I copy and paste the game’s PGN there for analysis. Multiple colored arrows show best/worse moves and their values. What if allows you to test alternative moves easy. I use about 10 hours a week. So cost per hour is 5 cents an hour. $20 a year.
Mediocre $: Chess coaches. The few times I tried a coach, all they did was repeat the obvious. About $20 to $100 PER HOUR. Expensive. If you go this way, expect to spend hundreds a year to get improvement. Maybe worth it for beginners.