I think the Whitehair experiment at Center is not happening again. Ideally we're able to move on from him this offseason; he's just not he same player he was a few years ago.
In your scenario, I'm probably taking Pittman, though Nelson is a close 2nd. Pittman is the youngest of the 3, and WR is the weakest crop among this year's free agent market and draftees. Buckner would have the most immediate impact as the 3T in this defense and he's an awesome player, but he's the oldest of those 3 guys, and I have faith in the Bears finding other ways to fill that hole, whether it's through free agency or the draft. Same with OG, even though Nelson would immediately become our best OL. A year ago I probably would have said Nelson. As for WR, this year's free agent class is extremely weak, and while the draft class has some solid Day 2 depth, in terms of adding a #1, Pittman would be our best bet. And that doesn't stop you from continuing to improve that position next year or the year after. If Pittman becomes your #2 because you've found a legit #1, that's fantastic. A WR group of Pittman, Mooney, and Claypool is far better than how we started last season.