there are as many different kinds of drums as there are cars. how many car brands can you name? there are equally as many drum brands. i like to separate drum kits into 2 sets.... you got your brand names, and your "off-brand". your brand names are top of the line drum makers.... respected and professional drummers play them. these include (but not limited to) tama, pearl, ludwig, mapex, yamaha, pdp, DW, spaun, ocdp, truth.... i could go on. off brands are significantly cheaper and are kind of like "knock-offs". these are aimed at beginners on a small budget. brands include sonor, royce, gammon, pp, cb, pulse, first act..... again, i could go on. the beginner series of a nice brand will run you minimum of 500$. if you get a knockoff, you can pay more like 200-500 for a full set. which brand you choose really depends on your budget and also your personal preference.
as for choosing the kit itself.... just look for a standard, full-sized kit. get a 5-piece kit (which refers to the number of drums). so thats a snare, bass, and 3 toms. some kits are sold with cymbals and hardware/accessories, and some are not. you need to make sure to read the fine print. most drum kits above 500$ are sold as "shells only" meaning cymbals and hardware are NOT included. which means you will need to find your own hihat, crash, and ride cymbals, and stands to go with it, plus a bass drum pedal, throne (chair) and sticks.
i would advise buying used. you will get a LOT more for your money. dont be nervous about buying used drums. drums are designed to be hit with lots of force. so chances are, used drums can literally withstand a beating.
as for learning, youtube is the best place for free lessons. i would also check out the education link at www.vic-firth.com as they have lots of free videos and sheet music to use. if youre willing to pay a small fee for online lessons (20$ a month) check out www.mikeslessons.com. he is great for beginners and advanced players alike. for a sample, check out drumteacher76 on youtube.
there is a TON going on in this question and i could keep on going. but its too much to type and you need to provide more detail to narrow your question down and then i can make my answer more detailed. feel free to email me from my profile page if you need further help and id be glad to do what i can :)