You're right. "Sharepoint" is sort of a misnomer. In fact, it's the only software we had a problem working with historically. It does not share well, and it used to be that we didn't coexist well with it.
As of FogBugz 7, we coexist fine with Sharepoint and all other generally available software that I've come across. If you have a proprietary site, there's a small chance there can be an issue, but it's very rare. More commonly, FogBugz doesn't share a site in IIS with Sharepoint well, but if you give it its own site it should work as expected. The problem was with Sharepoint's handler's getting "first dibbs" on requests that were really destined for FogBugz.
SQL Server Express should be just fine for quite a while, particularly if you're not heavy users of the wiki and if your customers aren't sending in large log files (or uncompressed bitmaps, as happens to us sometimes). Express' 10GB limit should be plenty. After that, you're talking about Workgroup edition, which goes for $2500 and removes any meaningful cap on database size.
Even if you do have lots of attachments, it'll take you a while to near that limit.