I can provide a little perspective on a newbie's experience with the AMM, as I'm actually in the process of working through my requirements to reach the Bosslopper level (which is the lowest true membership level where you have a member number). So right now I'm probationary, called a Pilgrim. You do have to have an invite, but I didn't find that too hard once I approached a couple of members and went over my background and experience. The 3 years of membership thing is for reaching the highest level, Hiverano, which means you've been a Bosslopper for 3 years and have done all 20 requirements rather than just 10 requirements to become a Bosslopper. Yes, that's a little complicated I guess. My 2 year clock to complete my 10 Bosslopper requirements started back in the summer, and I'm clearing hurdles and expect to be done by late summer. Tomorrow I'll be fleshing my first beaver taken with period-correct traps and methods. Yes, it's been a time commitment, though I already had some of my gear and a decent stack of braintan just from having a strong interest in all this since my teens in the late 70s. I'm 57, and am a part owner of a small consulting company here in eastern Idaho, so that has afforded some flexibility to be able to take off the extra time needed to work on requirements, but mostly I've been able to do what I need to do on the weekends. Unlike most of the members I've met, I was never previously involved in a buckskinning group, I just did my own thing with a hunting orientation; that's not the norm.
As far as the people in the organization, I've had only limited exposure, as there aren't many active members in my area at present. My sponsor is a really nice guy, and he and I briefly attended the National this past summer. The people I met were mostly very friendly. I've also met a few AMM members at the living history event at the museum in Pinedale and at Ft. Bridger; a few seemed a little aloof, but most were not. I'm enjoying working through my requirements and am learning a lot, despite being a lifelong backcountry hunter. As far as gear and costs, as I said I already had some things, including a hand made FL, but it is a little pricey to fully gear up if you are trying to get set up fast. If you take a little more time and make most of your gear yourself you will save a good chunk of money. If you make the jump to being mounted you are really going to spend some serious money.
One of my personal interests in all this, aside from gaining the knowledge, gear, and skills, is to hopefully make some friends who are interested in period correct hunting, but the AMM's strong commitment to authenticity is also a strong draw for me. With that said though, my impression is that most of the members tolerate some inaccuracy amongst new people if they are showing that they are making an effort to learn and improve. As far as the whole gun question, you can definitely document caplocks pre-1840, and the ledgers show a lot of percussion caps going west in the late 1830s, so I think you'd be fine with that kind of rifle. Everything I've heard is that if you can document it as pre 1840 you're good. I saw a Patterson cap and ball revolver in a guys belt at the AMM National, which is pushing the 1840 limit very, very hard. Sorry to be so long winded.