well with the GH2 you would probably want to install magic lantern or "hack" it in order to get that amazing quality that everyone brags about why the GH2 is so amazing. it is true that after hacking the GH2 and installing magic lantern the GH2 will be able to crank out some extremely impressive video, but hacking your camera is a little dangerous but not very but you do run the risk of ruining your camera if you do it wrong. the hack gives you a higher bit rate for your video which basically is what makes the video look a lot higher quality.
now i cant find it exactly on the manufacturer websites for both cameras as its a detail not needed by majority of consumers but right out of the box the canon T3i will beat the GH2 in bitrate (this does not mean overall quality of everything) but the T3i has a bit rate of roughly 45mbs and the GH2 has a bitrate of 25mbs but after the hack the GH2 surpasses the canon.
i personally do not suggest the GH2 while its a fantastic camera its a micro 4/3s camera. this is not a bad thing just not ideal. here are some lenses that i would suggest. i am not going to suggest 3rd part lenses and this is just for the GH2 or canon camera that i think would be great for you to get started so you can get a feel for price. these prices are from manufacturer websites to keep it fair i guess
now i wont comment on overall image quality achieved by these lenses as i am not familiar with lenses for the GH2 and honestly the differences are not ground breaking in the lower price range for camera lenses.
14-42 kit lens $200 http://shop.panasonic.com/shop/model/H-FS014042
14-140 kit lens $850 http://shop.panasonic.com/shop/model/H-VS014140
35mm prime lens 3rd party can be bought around the $300+ price range
a lot of the panasonic lenses on their website ballpark around $1000 or $300
18-55mm kit lens $200 http://www.usa.canon.com/cusa/consumer/products/cameras/ef_lens_lineup/ef_s_18_55mm_f_3_5_5_6_is_ii
55-250mm $300 http://www.usa.canon.com/cusa/consumer/products/cameras/ef_lens_lineup/ef_s_55_250mm_f_4_5_6_is_ii
50mm f1.8 $125 http://www.usa.canon.com/cusa/consumer/products/cameras/ef_lens_lineup/ef_50mm_f_1_8_ii
all of these lenses from both companies can be found cheaper used of course. but this gives you an idea of the additional prices for lenses you might need. i did not cover all lenses these are just examples and are not what i am saying you should buy just options that are available.
this microphone is insanely popular and will be highly recommended on every forum you check. sennheiser also has a version of this mic that costs more but rode is not a cheapo by any means they make a good product and i dont think you need top of the line pro audio gear since audio gear gets crazy expensive. http://www.bhphotovideo.com/c/product/744768-REG/Rode_VIDEOMIC_PRO_VideoMic_Pro_Compact_Shotgun.html
here are some tripod options that would work for you for both video and photos of nature and documentary and interviews: (these are just options and again not saying these are only what you have to chose from, note these are pro video tripods not photography ones but honestly both pro video/photo tripods are equally expensive although at a certain point pro video tripods can get well over $2000)
just some tripod samples at a certain point the price just jumps to $1000+ for the type of camera you are looking at then jumps again to $3000+ for ENG and studio cameras.
i think that covers everything you might need. sorry for not being more helpful but i was bored and felt like making an example out of the other guy and troll him a little because he did a terrible job helping you and still is yet to provide anything helpful for your questions lol.EDIT:
on a side note whenever most of the knowledgeable people of the photo or video section here on OCN give camera advice we generally suggest for beginners such as yourself to see how many of your friends use canon/nikon as they are the most popular brands for DSLR and if you have canon friends you can borrow lenses and accessories from them and same for nikon. when it comes to video nikon is not shabby but has only recently made cameras that are worthwhile for professional video, the lower end nikons that have video are still great for someone like yourself though. canon is slightly more affordable for beginners but nikons are not that much more expensive.
the D5100 would be my suggestion for nikon and it comes with a 18-55 kit lens and you can get a 55-250 for $250. for canon the T3i is the newer camera but the t2i will have the same quality video but both can be bought with the 18-55 kit lens and a 55-250 for about the same price (a T2i would save you money over the t3i especially if you buy refurb from canon). the major difference is price in camera body. now i do want to note that the D5100 is not the nikon equivalent to the canon t3i to the best of my knowledge i am not 100% but they are about the same price with kit lens Edited by Conspiracy - 3/19/12 at 6:36am