Looking at a second bass. Fretless or no?

Fretless basses are pretty versatile and you can cop a lot of different tones with them, so I wouldn't worry about one-dimensionality of sound.
But as my hearing is better than my intonation, I sometimes find practicing with the thing for a length of time can sometimes engender a certain queasiness. Which is to say, you might want a #3 for when you're not feeling fretless but still want a bit of strange. In general, though, only good things
to come from tackling a fretless -- including a newfound appreciation for the relative "precision" of the fretted note.

 

That being said, fretless is definitely one of the more distinctive bass sounds, and one that the typical non-bass playing civilian is more apt than not to
actually notice -- and so while fretless might not become your main sound, it could well develop into a essential gimmick, at least for a song or two per album/set.

Here in L.A I see used MIM Fender Fretless Jazz basses on Craigslist every week in the $200-$300 range. Well worth a flyer at that price, and you can always throw it back if it doesn't suit you.