I'm talkin' about the near-guitar and outside-guitar type instruments here: the banjo counts (in my mind), as do the Dobro-style guitars. Arguments can be made for mandolins, lutes, and ukeleles. I'm excluding these instruments from this page's discussion of acoustic guitar types because they're not likely to be your FIRST purchase (MAYBE the ukelele. Maybe). Each of these instruments has a dignified place in the cosmic orchestra, sure, but they tend to have very specialized uses. In general, beginners who want to learn a string instrument will start with a guitar.
I really feel like I have to make a special mention of Dobros, though. These are generally acoustic guitars set up for either fretted or slide playing. They differ from normal acoustics in that their bridge is connected to a resonator of some sort, typically made from a plastic cone. The resulting tone owes something to the banjo in its character, but has a little more sustain.
Still, Dobros are a relatively specialized instrument. Unless you know that THIS is the sound you need or are looking for, I would suggest looking elsewhere for a first guitar. If you already have a 6-string, and possibly a 12-sting in your guitar army, you might consider a Dobro as a textural change of pace. But they are probably not best suited for "first guitars".