You probably want to pay the most attention to the one where the work is not physically taxing and they give you money for, eh?
I'm with you: I won't allow Oracle on the property.
Now, depending upon the industry, you might want to look at Informix (big in transaction processing -- like, say, NASDAQ, WalMart, banking, finance). Informix is sort of the granddaddy of PostgreSQL (the C API, used to be called ESQL/C, for Extended SQL for C, was developed by Informix and is included with PostgreSQL under a slightly different name). If you like PostgreSQL, you'll love Informix.
MySQL? Well, Oracle owns it, lord knows what's going to happen to it (Larry Ellison just doesn't believe in giving something away that he can charge for, eh?). Not bad, kinda primitive in some ways but getting there.
There's DB2 if you're stuck in an IBM shop (and heaven help with that peculiar product; oh, yeah, IBM owns Informix nowadays and they're doing a good job supporting and enhancing it).
Ain't much else worth a hoot for big-time shops but there are some nice little "lite" offerings.
And, heaven help you, stay the hell away from any crap from Microsoft -- affectionately know as Squeal because of the way it makes processors howl whey you ask it to actually, you know, do something?
Hope this helps some.