Obviously its possible to physically play both power chord/rock songs and more introspective acoustic pieces on any guitar but if you are wanting to create different sounds in those styles there are a few choices available.

Firstly if you simply want an acoustic guitar then consider a jumbo sized instrument for the big power chord songs and then a parlour (very small body) guitar for playing on your own. Parlours are great for finger picking as they have less bass response and are really comfortable to sit and play around the house. Although, if you only have a few hundred dollars I'd be inclined to buy one better instrument rather than two cheaper ones.

Another alternative is a hybrid guitar. Hybrids tend to be classed as small bodied electric guitars that that also have an acoustic 'voice' by using combinations of chambered or hollow bodies, special acoustic sounding pickups and bridges or even have a built-in digitally modelled acoustic sound. The quality and style of sounds vary wildly, as do the prices so check out as many models as you can - even look at those out of your price range to check out if this is what you really want. Hybrids are mostly a bit of a compromise and probably won't replace a good electric or acoustic, especially at this price range, but are wonderful for a wide variety of instantly accessible sounds if you haven't got a guitar tech to hand you a new instrument after every new song! So try out a few of the suggested guitars below as see if any of them work for you.

Fender Nashville power telecaster - basically a good Mexican made Tele with a piezo acoustic bridge. This is good for great electric sounds and 'plugged in' pseudo acoustic sounds for the odd song. Not that suitable if you want a great acoustic tone at home but a good all-rounder, and - Tele's never go out of tune!

Line 6 Variax - this is a modelling guitar that digitally reproduces the sound of 27 classic electric and acoustic guitars. You can customise the sounds and even the tunings and recall them at a twist of a knob. In my opinion the electric models are better than the acoustic and you'll also need a good amp and PA to get the best out of it. They also do an acoustic-only Variax which has fuller acoustic voicings and may give you the sound choices you are looking for.

Musicman Axis Sport - you may just about find a used one in your price range. These are the most beautifully playing electric guitars that come with an acoustic bridge option. Again the sound is pseudo acoustic so only look at this if you want to play more electric and use the acoustic sound for the odd song.

Taylor T5 -Taylor seem to be the first company to produce a hybrid guitar with its feet firmly in both camps. It does cost a lot ($1400 upwards used) but through extensive research and development they have managed to create a great guitar that sounds and plays wonderfully as both an electric and acoustic. Fishman Power Bridge - This system (which appears on the Nashville Tele) can be bought as a standalone item and added to many electric guitars to create an acoustic voice. You'll need to get a professional repairer to fit it for you unless you really know what you're doing.