Is a cutaway acoustic guitar worth the bother?
Above are two dirt cheap acoustic guitars, the Jasmine S35 and the Jasmine S34C. And when I say dirt cheap, I mean it. Check the links to see for yourself. (And surprisingly, both guitars get really good reviews.)
The S35 is your standard dreadnought acoustic shape, and the S34C is the cutaway shape.
The only reason the cutaway shape exists is to have fret access above the 13th fret.
On an electric guitar, it makes total sense to use a cutaway shape so you can access all the frets on the neck.
On an acoustic guitar, it makes no sense at all to have access to the high frets since you will never play there anyway.
Now you might think to yourself, "Oh yes, I would play there all the time!" No, you wouldn't. If you own an acoustic now with the cutaway shape, try playing notes on those frets. Yeah, sounds pretty terrible, doesn't it? That's because it's an acoustic and not an electric. There are no pickups compensating for that "bitey," nasty tone that sounds like a kid's toy piano up there.
On the acoustic, it is very unlikely you will ever play anything past the 7th fret, or maybe the 9th fret if you're adventurous. When you want your notes and chords to ring loud and true, you don't play anywhere above the 7th fret so you can keep as much definition out of the sound as possible.
You can't apply electric guitar thinking to an acoustic. Many try, all fail.
Of course, there's always That Famous Acoustic Player someone will mention that plays really high on the fretboard with his cutaway acoustic guitar. Here's a news flash for you. You're not that guy, and you will never be that guy.
The standard full size dreadnought shape always sounds best
This beginner's bundle, the Yamaha FG700S "Folk" Bundle:
...while costing more than just the guitar itself (which by the way gets a top 5-star rating even though it's cheap) is a darned good deal.
Why do cheap full size dreadnoughts get such stellar ratings? Because they're built traditionally. This style of guitar was around way before the electric was, and through literally centuries of building them, companies with modern machining and modern materials are able to build these things so well that even the cheapest models play and sound incredible these days...
...as long as it's a full size. Stick with the full size shape, and yes, it will sound good and project well. With a cutaway shape, you take your chances and usually lose.
"I want something I can plug in to an amp"
No, you don't.
Acoustic guitars always sound better from a microphone and not an on-guitar pickup. Remember, a standalone microphone (or a pair of them) is more close to what your ears hear.
If you absolutely have to have a pickup, get a Seymour Duncan Woody. Yes, I've mentioned this before and will mention it again. The Woody goes right in the sound hole and sounds great - but - I guarantee you will like the miked sound better.
Stick with the full size dreadnought
Sounds the best, plays the best, rests the best on your leg when sitting and it's not any heavier than a cutaway is since an acoustic dreadnought is lightweight to begin with.
You're not going to play solos on high frets with your acoustic. Get that electric guitar thinking out of your head. Stay with the full size shape. It has been proven for longer than you've been alive that it's the best you can use for a steel string 6-string acoustic. What more proof do you need?