One last post, I missed a bunch of posts so I apologize for all the replies in order.
So some general my thoughts about the various areas:
Ownership: Be it buying servers via donations, or holding donations to pay for monthly services, the question of who owns what and how they're accountable and such is something to consider. No one wants a situation where someone gets mad and takes their servers and goes home.

Not a pleasant thing to think about something that warrants some thought.
Hardware Source: As mentioned you can rent servers or buy and colocate them, so which path will need to be decided.
Reliability: In general (and users will of course disagree) I don't think the forum is a mission critical service requiring five nines of availability. So spending a lot of money on redundancy probably isn't necessary; depending on the service provider's or vendor's warranty and reasonable levels of backups is probably fine. A day of downtime while a server's power supply is replaced or the database drive is replaced and restored from backup is acceptable for the forum IMO.
Hardware: I'd suggest two servers, one for the database and one for the web server. An SSD for the database is a good idea, spindle drive for OS and database logs and SSD for database files. The web server doesn't require as much in the way of disk I/O, so two mirrored drives is sufficient IMO.
OS: CentOS is fine to use, lots of support and info out there. I think CentOS 7 is even available now.
Web Server: Apache works well and I'm not sure nginx is any faster for PHP performance. Static file performance is higher, but I think we should be offloading static resources to a CDN anyway, so Apache is probably fine, but nginx might be fun to use anyway (haven't played with it personally).
Database Server: As mentioned previously, vBulletin 3.x uses MyISAM table types, in which case I'd suggest MariaDB as the database server. It's a drop-in replacement for MySQL but has other things that MySQL either doesn't have, is coming, or is exclusive to the enterprise version. If we converted the table types to InnoDB then we could use Percona which is also a drop in replacement for MySQL. I prefer Percona but maybe that's just because I've been reading the mysqlperformance blog for a long time.
CDN: As mentioned using a CDN like MaxCDN can reduce the load on the HTTP server a lot (most of the requests in a vBulletin page are for static resources). Then the HTTP server can focus on serving up PHP pages. It's relatively cheap and there are a few ways to set it up, someone really skilled with rewrite rules can do it completely via rewrite rules. Personally I just changed the file locations in the vBulletin software itself; seemed easier to me.
Images: Related to that is images in general. These forums allow for images to be uploaded, and icerat mentioned that the forum DB is 32GB which seems quite high to me (my forum is 4.2GB for 5 million posts). If images are stored in the DB then yes that's a significant performance issue, and a storage issue too. In my opinion there are a lot of different free image hosts out there and this is a forum, not an image server. On my forum we simply don't allow image uploads other than avatars, if someone wants to show an image they can upload it to imgur.com themselves. But at bare minimum images should be on the filesystem not in the database, and the CDN could also be used to offload the request for images from the server.
Backups: Technical issues on how to backup the database aside, something like Crashplan ($10/mo business) is inexpensive IMO and gets you offsite backups as well (though Crashplan for Linux is a more complex setup). Some level of backups might also be included with whatever server or colocation plan is obtained.
All I can think of at the moment.