I have no idea what this mythical "straight" UNIX is (a Bell Labs tape on a PDP-11?), but if there's a kernel of truth to it, MySQL did/does 'assume' Linux, in the 'all the world's a VAX' sense, and
there used to be some minor glitches there.
I'm not even sure if that applies anymore, and I've yet to become a database wonk myself. People certainly run it, on all three BSDs.
The word from the horse's mouth might be a help.
As to selecting the 'right' BSD in this day and age... There should really be a 'product matrix' for this. Hopefully I've got the following right:
NetBSD 2: BGL SMP, high-performance threading, fairly minimalist, "everything you could need" in pkgsrc, portable. No linuxpluginwrapper, so use a Linux browser if you want Flash for desktop purposes. Unsure as to 3D direct-rendering support, might exist for everything !nVidia. Maybe a little shaky from the bump to 2.0, likely to keep doing whatever they've been doing as they always have.

OpenBSD: BGL SMP, fairly minimalist, secure, great for bastion hosts, firewalls, certain services. Looks like performance for some workloads may be a concern, if you actually care that much.
FreeBSD 5: SMPng, high-performance threading, buzzword-compliant security (ACLs, TrustedBSD?), "everything you could need" in ports. Still a bit warty from the whole 5.x adventure, may be continuing to improve in -STABLE. Hanging out with DragonFly people gives you too many things to be afraid of.

DragonFly: LWKT, LWT someday?, libthr-like threading as of this week. Infinite promise, while my current experience suggests you may wish to hold off 'production' use unless you know what you're getting into. The next -RELEASE (1.1?) smells like it'll be a stable starting point when it arrives, so if you're not already a BSD nut, get on the bus then. (...If you
are already a BSD nut, drag out some spare hardware and help shake it down!)
Linux: Looks good on paper. There is probably some specific kernel point release that, coupled with some specific distro, does what you want.
I'm at a loss to tell people where to start right now; each and every distro *will* do the job, while the caveats present no clear winner. (...and Linux sure *looks* like it's hit an island of stability right now, with Debian and Ubuntu seeming the moment's safe bets, but people who use it keep running to me with 2.6 horror stories...)
If you provide some sense of your mentality, astrological sign, and the lay of the lines on your palm, I might be able to peer into the crystal ball and make a guess as to which will be right for you. Otherwise, there's always the argument for picking something and sticking with it until you find enough reasons not to... which is how everyone else gets along, whether they realize it or not.