Noah, if you look a the tag in the soundhole, it should tell you the model number and serial number.
The Taylor 110ce is $700 new with the ES2 electronics. Its a dreadnought with laminate Sapele body, spruce top, maple neck, ebony fretboard. Taylor makes the 112ce-N which is a 100 series with nylon strings. It runs about the same.
I find that neck shape is a very personal thing. I have friends who love baseball bat necks. I need a thinner one, and don't really care for a V shape. The Taylor neck feels much better to me than the Martins that I played. I like the feel of Gibson acoustics, but sound wise, they seem to vary a lot. When they are good, they can be very good, but I've played some that just felt dead. In the end, it was a 310ce for me.
Taylor necks can be reset without steaming the joint, which is a big plus. Between the shim system and the truss rod, you can adjust them like a Fender.