The most well-known database for the Mac has been and still is FileMaker. Originally it was made by a few small companies until Claris bought it. When Claris went by the wayside, Apple took ClarisWorks and FileMaker, Inc. became a different company.
FileMaker is pretty decent. My experience with it has been limited but it seems OK. FileMaker II is easy to use but for most practical database purposes in a modern setting you'll want one of the FileMaker Pro versions. Check on eBay.
ClarisWorks is good for most databases. Since it was developed in the same place as FileMaker Pro it works as sort of a "lite" version. If you've got a newer Mac you can run AppleWorks. I've used AppleWorks 5 on my iBook G3 for most of my database work.
I've never used dBase on the Mac, but I found dBase III on the PC to be powerful yet awkward. I'd take it any day over Microsoft Access but I would rather use a FileMaker product.
I can't say I've used Full Impact.
Wingz, Excel, and 123 are spreadsheets, not databases. Wingz was purchased by Claris and became Claris Resolve. Resolve is my personal favorite spreadsheet (though that may change tonight when I go to an Apple Store and check out Numbers). Excel is fine for most things, although you're better with Resolve if you like to use graphics. 123 is cumbersome on MS-DOS, I wouldn't imagine it would be a whole lot better on the Mac. ClarisWorks has a decent but not exceptional spreadsheet module--although I've done some decent work on it. I'd rather use Resolve or Excel if I could. Excel is easiest to find of the three big programs, you can generally find this on eBay. Resolve is difficult to find, and Wingz harder, yet it's worth the hunt. The only 123 I've seen is one I got from a friend. The manuals were huge and in small print.
As far as a version of Excel, only use 1.5 if you've got a pre-1990 Mac and System 6. Verison 2.2 is the best pick for low end machines. If you can, get 3.0 or 4.0, both run fine on a Plus on up. I don't believe 5.0 runs on a 68000. From there you have 98, etc.