Expanding on what Toxic-Stars said about linear vs. circular polarizers:
You only need a circular polarizer if you're planning on relying on your camera's autofucus feature. If you preffer to manually focus, or if your camera is strictly manual, you're better off buying a linear polarizer. There is no end result (or in-use) difference between the two. They do exactly the same thing, and work exactly the same way, the only difference is in the layout of the microcrystalline bands in the filter coating.
Linear polarizers confuse autofucusing systems, causing them to focus in and out perpetually without ever "locking" onto anything in frame (the autofocus wants to focus on the linear crystals in the filter). The crystals in a circular polarizer follow a curved pattern, and so the autofocus ignores them. This means *absolutely nothing* as far as your exposure goes, it's just for the benefit of the autofucusing hardware.
Circular polarizers, however, are nearly twice the price of linear ones, so don't shell out for one if you're going to be focusing manually anyway.
As far as recomendations go, I'd say pick up filters only an "as needed" basis while you're learning. The polariser is the only really universal "must have". Research and familiarize yourself up front with what different filters do and can do by reading and asking around, and let that info hibernate until you need it. If you have an idea for a photo that you know you'll need a certain filter for, then get it. Otherwise you're just wieghing youself down early with extra kit.
A few extra tips:
Some filter types can be easaly improvised. Star filters are just a kindergarden-simple defraction effect, and can be made simply by lightly abrading a piece of clear plastic in a criscrossing pattern. Very nice soft-focus effects are possible in a number of ways, from lightly spraying a piece of clear plastic with clear satin enamel (check hobby shops for model building supplies, or even the paint center at Home Depot), to simply huffing on the lense before snapping the picture. A sheet of clear acrylic from a Home Depot type place will furnish enough "blank" filters for a Cokin type-system to last you a good long while at a fraction of the price of a single prefab filter.
Party stores and florists will have clear colored mylar for use as wrapping that can be used, and any good copy place will enable you to print a sheet of whatever color their (or your) graphics program can create onto overhead trasparancy films.
If you're using a digital camera, you can get around using color filters alltogether by exploiting the manual white balance adjustment option. Just use a color card instead of a white card to set the white balance. The result will be a filter effect of the complimentary opposite of your chosen color card (i.e. use a blue card for a red filter effect, yellow for green, etc.). A ten dollar book of double-sided scrapbooking paper can do the work of hundreds of dollars worth of color filters.
Have fun!