Ds 3 adores puzzles right now. He has some octonauts ones - ranging from 12 to 24 pieces that he does by himself (although I sort into piles for each puzzle). Even though he can do them by himself, he loves the familiarity of them, and does them several times a day. His other favourites have 15 to 26 pieces, and reasonably large pieces, although if he comes across a much harder puzzle e.g. at MIL's, he will be desperate to do those too, and I have to sit and almost hand the pieces to him in order, as the 100 piece ones are far too tricky for him.
Sometimes it's not the size and number of pieces, it's what's on them. You need puzzles where the picture carries on obviously from one piece to the next, so there are obvious bits to match up. One of Eliot's favourites has letters of the alphabet with a picture, one puzzle piece per letter, but on the sticky out bits of the pieces, you can see a little of the next picture along, so he can find the next piece himself. I have seen some really badly thought out puzzles for kids where there's a small picture and then most of it is a plain coloured border - very tricky as there are no clues!
I aim for puzzles that are just beyond what he can already do, and I sit with him the first time he does them, to help. I don't usually bother with edges and corners, as I think that's quite a complex way to do puzzles, and one that he can't do so easily on his own at this age. I encourage him to look for pieces that match - 'can you see the rest of the bear's hat?' 'What's that pink bit there?' etc, so that when he does it himself, he knows what to look for.
One other tip - make sure you buy decent quality puzzles! Some of the cheap ones have really thin pieces that warp easily, and it's impossible to keep the pieces locked together when they won't lie flat on the floor - very frustrating!!