If your friend is actually trying to blow 7k on a studio, I doubt he's looking to end up with no mics over $400 each. People have egos to feed and studios need some glitz to attract the occasional potential customer, paid or otherwise.
While it's true that with solid apogee converters, one Neve channel, good monitoring and soundproofing and a selection of dependable dynamic mics, one would have an easy time making good demos, it's also true that you're not going to convince a lot of people to use a studio where all the front end is stuff they could buy for themselves.
Ask instead how to spend 5k on a good studio, and then look around for how far 2k can take you on the used condenser mic market. I used to see U87s under that ceiling all the time. Wish I'd snapped one up. Wonder what's currently at that mark that will end up growing in reputation and/or value. I bet it used to be U47s.
I'm sure if you search for five minutes you'll find a ton of "best mic under 2k" threads. Anything close to that ceiling is going to be amazing.
DIY all the sound treatment you can. There's an ipod/phone app for rtas to check how the room is EQed. That will give you an idea of where to start changing the room acoustics.
Better yet, build a vocal booth with your friend, since it sounds like everything you're doing would fit in a booth, and you can get louder within small apartment walls if you put up more walls, even closer between them. That turns the whole room into an "insulating space" where the source vocal reverberates and dies out before your firend's neighbors hear a thing. It also keeps your friend's neighbors off your recordings.
But don't spend 7k on professional room treatment and leave only one SM7
as the cherry on top. Yes, most of Thriller was cut on SM7s, but it was cut on six of them, and a bunch of other mics, going into the most expensive tube mixer the world has ever seen.
If this were me, looking to spend 7k to turn a room into a studio, I'd start watching ebay and find out the price of reel to reel tape machines to get some old school mojo and Millennia/True/Earthworks preamps to get some modern clean tones.
I'd look for a DIY vocal booth plan, because everything you're doing sounds like it happens with one person singing and another person producing, and you can get louder and more natural in an apartment if you add some extra walls in the middle of the room.
I'd look at 1k of high grade, hand-made vocal booth (floated floor, space below the ceiling, no parallel surfaces, heavy plywood wrapped in rock-wool or heavy pvc, some room treatment inside), 2k of great vocal mic, 1-2k of great preamps and 2k of standard project studio. I'm sure you can search and find a ton of threads on how to build a workable project studio with 1k or 2k. You'll probably want to add a decent headphone amp with a couple of headphone extension cables running into the booth.
Yes, the above posts have a lot of good sense in terms of suggesting that you ultimately can't make good demos without at least decent tools in a lot of different areas, but I'm assuming that someone who starts a studio with seven grand is going to have a dime here and there in the future to add to it and make it better down the line. I'm also assuming that for that kind of an investment he wants a couple awesome things that he can point to right away and say, "look at this amazing studio."
To me, a properly insulated vocal booth with heavy-duty bass blocking outside and a few natural wood surfaces inside to give it a bit of sweet reverb... that would be pretty amazing.
A fancy, expensive microphone hanging inside it and a little window to give the producer a thumb's up after a good take... that says "come over and ask nicely if you can use my amazing studio."
Fancy foam room dividers say, "ask if you can borrow my fancy foam room dividers." Which might be more your style, since it's not your studio anyway, but I'd still rather be able to borrow a kicking vocal booth with an amazing mic and a great preamp than a whole lot of above average stuff.
With a great preamp and a great mic, you can put down great tracks. Then if it really blows up, you can get them mixed somewhere that has $10k monitors and racks of proper mixing equipment. Or if it kind of blows up, you can go and start upgrading your own stuff. But with 7k, you want to figure out one strength your studio is going to have and develop that. If that strength is "tracking singers and guitarists," then you need 1-2 channels of great mic/preamp and a good booth. Who cares how new your computer is?