Re: one question and one request
If you want to make AMVs, recording is not the option. Recording would be to use for a let's play of a game or tutorial of something computer wise or maybe to talk about fan theories while providing the actual webpage on the screen. If you want to record, I really can't help you there, but here are some AMV tips.
The right program: There are tons of programs. Some are free, some aren't. More expenseive and programs that actually cost something are better. You get more effects. You're paying for better. However, you don't need money to make a fanastic video. Windows movie maker 2.6 and Windows live movie maker are free. The former has tons of plug ins and many people use it and the latter runs tons of files and is really easy to use. There are alternative ways to get the priced programs, but I'd advise against it.
Getting clips: You can download episodes of whatever you want from the internet. Trust me, you can find out how and anything you want is out there. Just have patience. Some will be in mkv format. There are great free converting software. Freemake for HD and anything or Any video converter. I use both. Videopad is also a great side program to use on the side. You can basically use free programs to make what a priced one could do. You could also burn clips from a DVD. I believe handbrake is the best tool, but I'm not familiar with that method. A quick Google search will help you.
Making the video: Patience, but most important, be motivated and have an idea, a story you want to tell. I can't stress the latter enough.