I'll agree with the general consensus that the inbuilt pickup sounds are not really very usable for recording (in my experience and for the guitar sound I am going for - your circumstances/tastes may be different!) But in most recording scenarios, I believe this to be the case. I wouldn't even bother trying.
As for microphones, you have two choices - dynamic and condensor. Dynamics are typically not used as a primary acoustic microphone (they can have their uses, but generally not used). So your best bet is a condensor.
Any cheap (but studio type design) one will sound miles better than what you have now. Generally $150 will get you something that is capable (With the right recording techniques) to get you 90% of the way there.
Now unless you have a very nice room to record in, you'll probably want to record it dry (without the sound of the room) and add artificial ambience/reverb later. Chances are, your room is not very nice acoustically speaking. Hence you'll want to get blankets, mattresses etc set up around you to deaden the recording space and allow you to get a clean signal.
Do NOT point the mic at the sound hole. It will sound boomy and no good. A lot of the brightness and crispness can be had from aiming the mic around the 12th fret (assuming you're not using a capo). You're aiming for about the half way position. So if you've got a capo on 4th, then more like 14 or 15th fret might be a little better. Play with it and see.
The fullness and body comes from the body (duh!). If you're just recording acoustic and no other instruments, this is probably highly desirable. This is where a dynamic mic may work well alongside a condensor on the strings. But not always. A condensor might also work too. If you have lots of other instruments going on, micing here may not really get you the sound you need. My guess is this parahgraph is probably not overly relevant for you at the moment - but it's there just in case. You can likely skip this step.
NEW STRINGS ARE A MUST!!! I personally like the 80/20's over the phospher bronze as they are a bit brighter and for the sound I go for, more suitable. Choose as appropriate.
All the above should get you a great sound. It should be very listenable and workable. There are further things you can do to take it to the next level (better mics ect), but master the above and then decide when you're ready to try and take the next step up.