I have an Android smart phone (iPhone would be good, too) with unlimited online access. This is wonderful. But...the unlimited acess is around $40/month. I can't justify it just for chess. But I can justify it for other stuff. You have to decide this, personally, too.
With it, I can download just about any chess engine...anything I can on a desk top or lap top, including chess.com and all its features, including game play, tactical trainer, forums...everything. And, the screen size is quite adequate...no squinting, even with my old eyes (have had cataract surgery, even).
I also downloaded a free chess engine...there are many. I haven't downloaded any of the "for purchase" ones, yet...because I already have these on my laptop or desktop. Quite doable, though.
If you don't want to have unlimited access...I don't see why you couldn't put a chess engine or database on it, anyway. Simply pay the cost of air time to download it...what, 5 minutes or less? See? Or, maybe you could sync something over from your desk or laptop.
This is not the future...it is here. Fantastic!
What is the best? Ideally I'd prefer an Iphone or Ipad but those can be quite expensive if we count the contract. I also don't have personal experience with them. Is there a way to get an iphone without contract and use its wifi capability to download something like Stockfish?
What are some other decent Chess handhelds?