Okay, first of all, AMD and Nvidia both had driver problems so there is no point in telling that AMD had driver problems. I, myself have a 7950 (check my rig in my profile) and in Battlefield 3 I get 60 fps with 4X MSAA and at 1080p. Minecraft is very poor in graphical game. You can max out Minecraft with even a 7770. With a 7950, you will get well over 100fps on maxed out settings. The 750 is the second best AMD single graphics card on the market right and to be honest, I never had any trouble with their drivers and GPUs.
The 7950 competes with the GTX 670.
Take a look: http://www.tomshardware.com/reviews/gaming-graphics-card-review,3107-7.html
Don't bother about the 6990, GTX 690 or GTX 590 or the 7990 because they are actually two GPUs. The GTX 690 for example is actually two GTX 680s.
Skyrim wont be any trouble maxing out. You wont get any lag.
Also, I am not a "FAN BOY", I used both GPUs and currently, I think AMD has the GPU market in terms of performance for money.
You wont need 16GB of RAM. Games yet don't even utilize 5GB of RAM and since you are going to be recording, 8GB RAM will be more than enough.
Don't worry at all about Minecraft. This game is not as intensive GPU and CPU wise as you think. You wont have any problem with this graphics card.
EDIT:
I might or I actually did over-exaggerated the fact that Nvidia had driver issues. Nvidia never had driver issues, but I never had any issues with AMD drivers up till now and I just don't want people to be misguided by the fact that AMD "has" driver issues. That is just wrong and that is the experience of an individual. Sure, AMD did have driver issues before, but if you look at it now, there is none.
EDIT
I see you want more opinions from more people.
Your really don't need two 7950 because it is too overkill. A sound card is not needed because the mobo comes with one and I am guessing you aren't gonna do some high music stuff (sorry I have no idea what to call it) so you wont need it.
Since you wont need that maybe you should get a 7970. You see that benchmark from techpowerup I gave you? If you look at all the games they have tested, you can see that the 7970 wins in 12 of the total 18 games tested. It even wins in BF3. I would get the 7970, but I am pretty sure Nvidia will release their new driver soon, so it's your call.
EDIT:
My bad, here is the benchmark:
http://www.techpowerup.com/reviews/AMD/Catalyst_12.11_Performance/6.html