bg, let me offer you a few ideas coming from an entirely different direction than Mike. I started with a team much like yours, no current hope and very little existing talent. I had two things you didn't... first, a previous owner had been with the team for one season and had already started the cleaning out process. That was a decent advantage. However I still had a few turd contracts on the books... most people do, I would think. And I picked up a few players I shouldn't have, not realizing they weren't worth it... I think everyone does that at first, too.
Second thing I had was, I thought this thing looked way too hard for me to figure it out by myself, so I got a mentor before I even got my team. All I wanted was NOT TO SCREW UP while I was learning. Think I've done OK so far. So...
Seems like you have a mediocre situation, and talent you don't like. There are pieces there you might not be able to move. Take your lumps at first. If your players aren't performing, watch them and figure out why. If your team sucks and you can't get out of it, use it as a learning experience. Plan when you can get rid of the parts that don't work, and plan what you'll do when it happens.
Probably the biggest thing I continue to learn is how to value players. Who will really perform, and who will just look like they might. That informs everything else you end up doing. But one of the other aspects of that is that you learn to realize just how much player talent is replacement level talent, and available more cheaply than you might expect. As I said, I started out with only a couple of true big leaguers, but I've at least filled out the team around them with castoffs via Rule 5 and Waiver claims. Get cheap where you can, as fast as you can. Sorry for the rambling, just trying to give you a little support.