Color Correction?

Definitely use DaVinci, that program is awesome.  You can edit your timeline and then when you are ready to bring it into Resolve, export the timeline as an .edl or .xml or whatever that is.  Then you can create a timeline in DaVinci and import that file and as long as your original clips are all in the same folder it should be pretty easy.

Or you could color everything first, then export it and then cut it up in premier how you want.  That way takes more space because you have the whole clip and things you may not need.  It's a bit clunky from Premiere still but those are a couple options.  It's definitely worth grading and correcting in there instead of Premiere though because you have much more control over the colors.

The style that I'm in right now is to have pretty life-accurate colors or even a little more contrasty. What I do is shoot in the Marvels Cinestyle (which people say doesn't really help, and I could agree, I just like the dry, flat look before delving into coloring). I only correct/grade in Premiere along with my timeline. Usually what I'll do is use Color Corrector Three Way and sometimes Fast Color Corrector to adjust white balances so all of the clips are within reason, then I use the Luma Curve to brighten the whites and crush the blacks a little. If a clip is less exposed than another, I'll use brightness and contrast to even everything out.