Yup, the 18-200 is rather slow, but good lord, it's an 18-200, and it has VR (not equal to a faster lens, I know, but often times it works wonderfully).
Anyway, on to the OP's filter question. Most photographers would agree that a CP is one of the most important filters they use (assuming they shoot outdoors), not only for eliminating reflections and darkening skies but also just acting as a ND filter on bright days. The more expensive filters have advantages, in my experience it's mainly that they're coated well and don't introduce new ghosting and flare. They cost limbs though (especially for the 'professional' sizes of 72+mm), so my personal route is to get decent well made filters that aren't coated and expect to use the hood and/or your hand here and there. In my experience there's not a noticeable difference in image quality unless you're shooting into light, in which case you must take precautions.
I take the same route with protective filters; I don't use lens caps because i don't like wasting time fooling with them (or remembering where the hell i set it down), so i use cheapo protective filters 80% of the time. They add lots of flare though, so I take them off when shooting into lights or the sun, or if I will be shooting something important continuously for a while. I broke one early on, probably saving a $400 lens, so I've bought one for every lens i've had since.
Singh Ray etc make great specialty filters as well, warming polarizers etc, but I've found that these smaller changes can be made acceptably in post processing. Unless you have all the time in the world when setting up and shooting your photos, only the more drastic filters should be used. I'm usually hurrying when taking photos, trying to frame correctly, get a decent exposure, sometimes not be seen (I really hate being yelled at for taking photos from public property by some yokel or overzealous security guard who doesn't understand the laws pertaining to photography) etc, and screwing on filters in the field is more than a slight pain (namely when I'm in a kayak, I love paddling and photography, but the two don't always mix very easily). When I'm shooting somewhere I'm completely comfortable and don't have to worry about lighting or weather, it's always best to get as close as possible to a finished shot in-camera.
Some no-name filters are probably good quality, but i haven't had any luck with them. I was going to get a $75 77mm Hoya CP but ended up getting a similar tiffen as a gift. It's even cheaper I believe, but it has worked very well for me.
This advice probably won't matter much for you since you'll be shooting with an 18-200, but I've always bitten the bullet and bought the largest filter size I need and used $5 adapter rings to allow their use on my smaller lenses. I figured I'd want to use all my filters on my Sigma 10-20mm, which is 77mm, so I just buy all my filters at 77mm, then use step-up rings for my 52, 62 and 67mm lenses.