Err.. a lens would be a good start, I'd have thought..
After that, which filter sort of depends on what you want it to do.
Bit of legacy from film is the permanently attached UV or Skylight filter. Ultra-Violet light is outside the visible spectrum, so we don't see it, but, 'film' can, so particularly strong UV situations (out-doors) could over excite the silver halide and make pictures come out a bit over-exposed. In doors, under tungsten or fluorescent lights, not a problem really, but if there's no UV light around, then there's nothing for the filter to filter, so let in all we wanted anyway, and we''d leave a UV or Skylight on the front all the while, 'cos they cost a fiver, where lenses cost a lot more, and they could save the front element getting scratched.
Legacy then, is still to fit a UV or Skylight on a lens used on digital.. digi-sensors don't work like film, and are actually 'tuned' to visible light with filtering screens in the chip, and so exposures tend not to get fooled by strong UV, so not really 'needed'... but, still cheaper to replace than multi-coated lenses, and marginally useful for 'protection'..
At which point we get into the age old debate about what's the point of having £500 worth of precision ground glass infront of your camera, if you then stick a 'cheap' bit of £5 picture glass in front of it to distort what it sees, and caus 'flare' .. use a hood and look after the lens properly....
Personally, I dont see the two as exclusive, you can use a UV 'protection' filter AND a hood to eliminate flare, and still cheaper to replace a UV filter than an expensive multi-coated lens, and my photo's probably aren't going to be so wonderful that any-one will grumble by the minute amount of IQ reduction one may cause.. and if I ever get to a situation it might make a difference... well, I can always take it off!
Otherwise... 'best' filter depends what you want to do...
I use a polarising filter to saturate colour in strong sun, and reduce unwanted reflections off car bodywork, or motorbike chrome or water and 'stuff'; Grey-Grad(s) to hold back bright sky in landscapes, balancing brightness between sky and land... and not much else these days. Those two you cannot 'replicate' in photo-shop post-process, though, while the cult of the one-touch 'insta-grimace' effects filter has pretty much made most 'primary' effects filters pretty redundant in the over-load of 'cheese'
Only other one you cat rally replicate in post, is 'Neutral-Density' or 'big-stoppa' filters that darken the whole frame so are often used to allow extremely long exposures and turn nicely babling water into a milky cliche'd mess.. but since that ones almost as cliche'd as the soft focus soft spot, vignette sepia toned insta-grimaces, I tend to avid them too!