Just some thoughts....
* what you want to do will be tough for $200 total. I like Armistice's advice - save more.
* you do need some sort of interface to plug the mic and guitar into... there are some cheap ones out there. Check out M-Audio and
Cakewalk V-Studio 20.
* do you want to record vocal and guitar separately? That's typical. One mic could work, but the majority of decent acoustic guitar recordings are done with 2 small diaphragm condensor mics. There is a ton of info about micing acoustics on the internet. You can use a single large diaphragm mic ... that's what you'll want for vocals, anyway. Results on acoustic guitar are different than with 2 SDC's.
* recording the direct output from an acoustic guitar's built in electronics is usually very un-acoustic-like. Some might even say "gnarly." You won't want to record that way for very long.
* built in acoustic guitar electronics DO work well in a live setting. So, one large diaphragm condensor for vocals and the built in electronics will be fine for live. Take a look at the Rode NT1-A and do a comparison to other mics like it. There are cheaper mics, but it's one that produces pretty good results for the money.
The road to producing satisfying recordings at home is a long, frustrating and (hopefully) satisfying one. It takes a LOT of research, a steep learning curve and making some purchasing mistakes along the way. From a gear standpoint, it can easily become a black hole for your money.
Some other things people don't realize they need until they begin assembling a home studio... decent headphones that don't "leak" sound that will bleed into other tracks as you record, mic stand(s), XLR and 1/4" cables, effects (either plugins or hardwware), reference monitors. Ah... the list goes on.