This may not be the most realistic of hopes, but here goes...
The Bears should do everything they can to lock down Super Mario or some other talented edge guy (although there's nobody else that even comes close) to compliment Julius. If the Bears can manage this there won't be as much need to address the secondary because plays won't have time to develop. You don't need great Corners when QB's are running for their lives right out of the gate.
Once the pass rush is zeroed in it's time to address the offensive weapons. Go get Dallas Clark. He's 32 but he's got great hands and some speed left. The draft is light on solid TE options, and the team seems to have a great deal of faith in Davis so Clark offers a bit of a stop-gap while we wait to see what happens. It would be great to see a second tier WR come in as well, I like Laurent Robinson's upside.
When it comes to the O-line I don't think the Bears have quite as much to worry about as so many of us seem to think. Once the line didn't have to worry about protecting Cutler for 26 seconds each play (exaggeration, I know), they actually played pretty well and Carimi is legit. I know, I'm as big a Badger fan as I am a Bears fan and this kid is the real deal. Garza isn't Kreutz but played good ball, Spencer is a decent Guard, and Lance Louis is as versatile and significantly better than Omiyale. Williams tends to lack consistency but can play when his head is right and he's healthy. Webb seems to have the trust of the staff even if he makes me nervous as hell. Can I say hell? Although, a little competition at Tackle could go a long way.
If there's a run on WR's in the first, then the Bears should grab whoever is best at the position in the first because that is by far the most glaring need. Earl Bennett has great hands when Jay's throwing him the ball but he's not a game breaker. The second-tier guys I mentioned earlier could set up opposite our first round guy (I hope Floyd makes it to us but I'd take Wright or Hill too) while he develops and Cutler would still have plenty of reliable options. The second round would be a great place to look at a CB or another O-line guy (good interior linemen should still be available at that point).
Then again, that's just the opinion of a bored fire fighter on a slow Sunday.