The diameter required for the filter is always written on the lens body.
There are different polarizers out there; For some time now you can find new onesnew ones which stop down the image by only one full stoponly one full stop (i.e. you need 1/100 s with filter instead of 1/200 s without filter). Older ones consume around 1.5 or more full stops (i.e. rather 1/60 instead of 1/200 s).
Hoya calls them HD (like Hoya Pol. Circ. HD Filter, 52mm), I've got multiple of these and I can recommend them. For other branches you might want to check their specs sheet (or test before buying).
You should get a circular polarizer, but it's a long time ago when I last saw a linear polarizer, so this should happen automatically anyway :)