I don't think the cutaway has much of an affect on the sound, not so much as the size of the guitar, particularly the thickness of the body... the whole "try before you buy" thing is always the best way to go; you'll find a lot of subtle to not-so-subtle differences from guitar to guitar.
There's a couple of guitars I would steer you towards. One is the Taylor Mini:
http://www.taylorguitars.com/guitars/gs-mini/I haven't tried it, but its gotten rave reviews, even some of the instructors here have tried it and really liked it.
The other is this one by Martin:
http://www.sweetwater.com/store/detail/DCX1E/I've tried the Martin DCX1E. First, let me warn you that even though its a wood top, its other parts (back, neck, and fretboard) are made of composite materials... but don't let that put you off... it looks and feels great, it didn't require dropping an exotic tree in the Amazon Rain forest to build, and its not as susceptible to fluctuations in moisture and temperature as pure wood guitars. This thing sounded amazing, and that was after trying a lot of guitars, some really expensive ones too. The built in pick-up sounded great as well. Its more than double your price range ($699) but well worth it. At $300 you're probably going to buy a guitar that will be a compromise in both sound and quality, and you may want to up grade again in the not so far future. I think the Martin is a guitar that would do you for a life-time. I have a rare, hand-made 100% wood guitar worth about $2000, and the Martin sounded as good as it, if not better. I will probably get one myself eventually.
Good luck!