There's a few necessary ones for photo effects: Polariser, ND Grad, Neutral Density (ND), and probably one or two more. But the majority of filters can these days be simulated in photoshop such as the warming filters, or the coloured filters for film photography.
The filter most people use is a UV filter or a No Change filter. Just add a cheap piece of glass on the front of the lens to prevent things like sand, dirt, rain, animals' curious toungs, or little kids curious chocolate covered hands from touching very expensive lens front elements. It normally forms a ludicrously religious debate about protection vs putting a piece of glass in front of your lens.
One thing is certain, many filters do affect image quality.
Ebay is good given the prices you can get Hoya's HMC and SHMC line of nice coated filters for almost cheaper than you can get Hoya's cheapest non-multicoated filters in a normal photography store. Avoid filters without any kind of glare coating, they are just asking for trouble.