What's the best online chess-shop?

Upgrading online is fine, the sites given by other contributors are great, but I would recommend that for something like a chess set, you try to find a specialist nearby, especially if you are looking at spending any decent amount of money.

If you want a simple plastic set/folding board then they are largely similar and it will not make any difference. If you are looking for a good quality weighted set, especially wooden, then it is always better to make your choice hands-on.

Different weights and sizes are important if you are spending any reasonable amount of money and you need to make sure you buy a chessboard to match, both in terms of coloration and having squares of sufficient size to hold your pieces in play easily.

This is doubly important if you are buying a figural set, as base sizes can vary and a website's measurements and recommendations don't always hold up in terms of convenient play.

If you're after a simple, all-in-one set though (and there are some excellent ones out there in a variety of materials), then please, disregard my ramblings and listen to the other posters' excellent advice. However as someone who a) owns a comparatively expensive chess set and b) used to sell chess sets, if you're planning on getting something nice that you can leave on the coffee table, get hands on and see what you like.

The U.S. Chess Federation has an online shop that is dependable and has good products, plus sales help support chess.

http://www.uschess.org/

http://www.chessstore.com.au/