Most folks that record acoustic guitar want the sound of a good mic. Having said that, you still should be able to get clean and clear sound via the pickup(though the Taylor Expression system is not my favorite). How exactly did you connect the guitar? How high is the meter showing on the track? In general, a standard guitar cable should be okay, but acoustic pickups are often unhappy going into any input that is not extremely high-impedance(reason for many to use a DI box or external preamp/pedal made for acoustics). As for level(the meter on the track), aim for just reaching the yellow, and stay away from red. With most acoustics, running direct won't sound very good without some EQ, compression and maybe a touch of reverb(just enough so you can tell when its muted).
Your results with a mic can be a mixed bag. If the room is untreated(or poorly treated), even a great mic can give bad sound. With no treatments, get a couple of moving blankets(thicker is better) and a couple of mic stands with booms. Drape the blankets over the booms and experiment with placement. With decent headphones, you can hear when you get the mic in a good spot, so move until you like it. With only 2 blankets, I'd start with a VEE in front of you and just far enough away that you can still place the mic where you want(a foot away at the neck/body joint is a good starting point). If the floor is hard, get a small rug. If you have no mics yet, I'd shop for a used small condenser(although I have a friend that made some really good acoustic recordings with a Shure Beta87). If you're new to this stuff, there's a lot to learn, so try to have fun with it and don't beat yourself up. Nobody hits a homerun the first few times
