I'm starting to look around a little bit for my first shotgun, something I could use for hunting, trap shooting, 3 gun, and, well, everything else. I would prefer an autoloader
I'm sure you would prefer an autoloader, but unless serious 3-gun competition is really high on your list of "things to do with a shotgun"... then a good pump is a good place to start, and a Benelli is, arguably, the very best place to start.
The two least expensive semiautos that come to mind are the Mossberg 930 and the CZ 712 Utility. They are, for the most part, reliable, durable and well made, and have made modest inroads into 3-gun competition... in particular the 930 JM Pro.
As the JM Pro is only a bit more (MSRP) than your $650 budget... this might be the gun to look into... the 24" in particular. 24" is an excellent compromise length for all that you want a shotgun for, other than some would argue it's a bit long for HD.
One small problem is availability. The JM Pro is highly desirable for 3-gunners on a budget, and consequently, they are frequently difficult to find, and sometimes priced above MSRP.
Being a Benelli biased individual
... if you had a (much) larger budget and 3-gun was a priority, I would of course recommend a Benelli M2 24" field, modified by yourself (it's pretty easy to do the basics actually), or by a 3-gun 'smith like Taran Tactical, Accurate Iron or C-Rums.
If you had that mystically larger budget and were really feeling frisky, a gun that quite a few 3-gunners are looking hard at is the Firebird Precision MKA 1919.
C