Every new guitar I've ever bought came strung with 9's... your DBT probably has too.

I've always used Rotosound or D'Addario strings... both are fine. I've played on a guitar with Elixir strings, and just didn't like the feel of them. Each to their own.

You'll get a fuller tone using heavier gauge strings, but it's a trade off. I use 9's on the guitars I use for lead, and 10's on those I use for Rhythm when recording. When playing out I generally use 9's... though I am finding now that 10's feel more 'solid'... so may switch to them full time.

Your acoustic probably has 10's on it...