#1
I need an acoustic guitar for under $600. I have no idea where to start looking. I don't care if its acoustic or acoustic electric and I'll manly be playing acoustic rock, jazz, and blues. I've been looking at the Takamine G Series EG460SC NEX ROSE Cutaway Acoustic Electric.
And how would an acoustic electric sound through an ac30?
#2
you'll get much more bang for your buck if you go acoustic and add a pickup later. you can get an all solid and very good sounding blueridge http://www.maurysmusic.com/inc/sdetail/35952 or 000 http://www.maurysmusic.com/inc/sdetail/35949

you could get an all solid recording king - not as good as the blueridge perhaps, but i pretty much like recording kings. or you could get an epiphone masterbilt acoustic electric DR-500MCE - while i'm not masterbilt's biggest fan, it is all solid and it sounds it. there are a couple other masterbilts in your price range, too.

rosewood does cost more, but there's some all solid rosewood guitars to be had in your price range:
http://elderly.com/new_instruments/names/recording-king-rd-227-dreadnought--RD227.htm
http://elderly.com/new_instruments/items/RO27.htm
or for just a few extra bucks
http://www.maurysmusic.com/inc/sdetail/35941

one more worth checking would be this ovation
http://guitars.musiciansfriend.com/product/Ovation-Elite-1778-TX-AcousticElectric-Guitar?sku=620750
it's very bassy with the wrong strings, but with the right ones - i'd suggest dr rare pb's - it sounds really good.

an acoustic guitar doesn't sound that good through an electric guitar amp.
#3
I just helped my friend pick out a nice Taylor 110 that sounded fantastic. I'd advise checking out one of those, to be honest. Sounds and plays really excellent.
Gear:
Jasmine ES33C
Hamer Sunburst Archtop Flametop
Electro-Harmonix Big Muff Pi
Fender Frontman 25R
#4
I have read real good things about Godin 5th avenue, its an archtop and it works great for jazz. blues and to some extent even rock stuff. You can get a Kingpin version that has built in pickup or straight acoustic and add your own pickup. Not sure what they cost...

Another option is either a good Yamaha or Takamine acoustic electric - they have some of the best electronics in the industry. I played a few G series acoustic Taks and wasn't impressed - sounded a bit dull for me - but once hooked into an amp you can make it sound however you want to I suppose.

If you have an electric guitar amp your acoustic will sound muddy through it, but try it and see for yourself. I purchased Marshall acoustic amp and really like the way it sounds with my Ovation run through it.