I can store probably around 33 million files without seriously affecting lookup time (256 * 256 * 512 - I'm allowing a 50% margin), but backing up or transferring these files would be a major pain

Gee, I don't know, it would seem that making incremental backups would be easier than with a normal database.

But what about database searches? Seems to me that there I'd also have to have a marged copy of the text there in a processed (punctuation and extra spaces removed) format, and just searching the text as it resides in the database won't be much help.

I doubt if it'd help much. grep is a very efficient way to search inside a file, and its regex syntax seems flexible enough to ignore punctuation and whitespace.

But you definitely should be thinking about about indexed searching, where you make a reversed index of important keywords and a list of every post where it can be found.

Will storing the posts in the database instead of as individual files take up a lot more space

As a general rule, databases are wasteful with space. They all seem to be designed as if disk space was free: if your disk isn't large enough to hold the data, you can just throw more hard disks at it. So no, I don't expect databases to be space efficient, or even recycle wasted disk space by itself. Whatever you do, your home grown solution will likely be a lot more compact.

But be prepared to put a lot of effort in it. To make a decent database-like system from scratch is a lot of hard work, requiring a lot of nifty home-grown solutions, many of those which are simply part of a standard database system.