Well, there's really three ways you can go. 2d, 3d and 2d/3d.
First off, you can't simply ask people what you should do. You should make the game *you* want to play. This is the advice given by countless game design tutorials. If you don't want to play it, will anyone else care?
I'm not an expert on anything. I have however, played a game here or there
Examples:
2d:
The old lucasarts games, particularly Zak Mckracken, Maniac Mansion, Sam and Max. The original three indiana jones games plus atlantis. Gabriel knight 1. That clown one (the name escapes me)
(possibly the longest journey? it's been a while) Lots of others.. some of my favorites were Monkey Island 1-3.
And although I don't really consider them adventure games, I believe the early myst games were all 2d
3d:
Well this one is tough. I think the last monkey island was completely 3d. I think the third Gabriel Knight was too ( i haven't played it) Myst : uru was 3d.
2d/3d:
There's a couple but I think they're fairly hard to find. I believe Grim Fandango was a hybrid of 3d character models and 2d backgrounds. I just finished playing "still life" (great game until the ending which does not exist.. seriously.. they made a game with no ending at all.. no wrap up.. no .. sorry

Umm still life has 3d models and the backgrounds I believe are 2d.
...
Again I'm not an expert on anything... I can barely program in darkbasic right now... but here's my thoughts:
Go with your strengths. If you have someone who is a fantastic 2d artist (drawings, paintings, etc) then you are probably better off with a 2d game.
If you have someone who is a fantastic 3d modeler, then a 3d or 2d/3d hybrid might be best.
Unless you can create 3d models ala doom3 (I doubt darkbasic could handle it?) ... then 2d backgrounds will more likely be more detailed. Also

if you're really sneaky, I was thinking about this the other day, you could get hold of a digital camera, and use real life places for your 2d backgrounds

With this method you don't NEED an artist for the backgrounds

still need one for characters and animation though. (unless again you used pictures *GRIN*)
I hope something in here helps you find what you truly want to create. Good luck