I've just jumped into filters myself in a big way so have been reading up a lot, here's some of what i've picked up myself and from reading around:-
As i'm sure you've seen there are millions of different filters! But there are actually only a small number that could be considered "essential". For example you don't need to worry much about the coloured ones etc, pretty much all of that can be done in photoshop. I would say the only ones that everyone should definetly have are: Circular polarizer, Neutral density and a Neutral density gradient.
For landscape the main filters are neutral density gradients, this allows you to darken the sky (for example) so that you can get a more balanced exposure and keep all the detail in the sky as well as not under exposing the ground. They come in many different strengths, 0.6 being the middle and a good place to start. Then theres hard and soft versions, hard meaning an abrupt change from the dark part of the filter to the clear part, soft being a gradual change.
The cokin P series is quite a good place to start, you need a filter holder, an adaptor ring (whatever sizes you want to fit on your lenses) and then of course the filters. Theses filters are square/rectangular and can be used on any lens.
Then there is the circular polariser, these are great for giving nice blue skys, removing reflections and increasing the saturation of various objects (good in forests etc). However they dont work that well on ultra wide angles (10-13mm on a 1.6x crop factor like your camera). Very worthwhile investment though! If you want to use the CP on more then one lens it may be cheaper to buy one large filter, and then some step down rings for the rest of your lenses. Saves buying one filter for each lens!
As for brands, Hoya is very well respected. They have several versions of each type of filter (different coatings). Its generally true that you'll get what you pay for so I think its worth spending a little extra and getting the best coating you can afford. There are also plently of other brands, only one i've heard lots of complaints about is tiffen, so maybe avoid them and i'm sure you'll be fine.
There are hundreds of filters about. Many kind of unnessary if you learn photoshop. But good fun if you want to experiment a little more when you're out taking the pictures. I've found in much more fun playing with the filters rather then photoshop, which is why i've invested in a Lee filter system (yum). Only problem is you always want more filters and they cost soooo much!
Anyway, hope that's of some help!