As the question title implies, if I root my Droid Incredible, will I lose all of my data? I'm not interested in installing a custom ROM right now so will rooting cause me to lose my data? Also, which tool should I use to root the phone?
Short answer: no
Rooting -- if successful -- doesn't change any of your data, it just gives you root access.
Now, if you reflash your phone's ROM -- something you can only do with root access -- then, yeah, you might lose stuff. A lot of people automatically associate rooting with switching ROMs, since rooting is required. But you can root, and then do nothing, if you want.
I'm so lazy, I rooted and installed a screenshot app; but it was so worth it. [Okay, not lazy -- I just don't have the need nor desire for much else, at the moment. But if I want to, I can.]
Caveat: anything done really, really wrong can screw things up. See: Are there any risks to rooting a device?
I'd recommend using Unrevoked to root your device. I don't have a Droid Incredible, but I used this method on my Desire with no probs.
You shouldn't need to wipe your data if you aren't flashing custom ROMs. Even if you do wish to later, you won't necessarily need to wipe your data, and even if you do there are lots of options for backing up and restoring your data (especially once your device is rooted!).