Like Kid said, if you know the tires are bad, go ahead and replace them first.
I had a '98, and the previous owner hit a deer. The tires seemed mostly fine (I think one edge of 2 of them were worn down, but not yet at the marks), but I had similar issues as yours if I got above 65mph, which I would only do on the last 3 miles of my commute. I had the alignment done, thinking it was really out of whack and had messed up the tires. It was within the limits, but I had them do it anyway, and it didn't change things.
For the couple months I commuted with it, I just didn't get above 60 for those last few miles, and there wasn't an issue that I could feel or hear.
I still had my '92 and ended up selling the '98, but next on the list was to replace the tires, and then possibly the suspension. I know the next owner immediately replaced the tires, and I told him about the issue, but when I talked with him a month later he only complained that the rear locking diff didn't work....but by the sounds of it I think he just didn't put it into lock the right way, and then had his mechanic start snipping wires. That was a sad end to something that had worked fine for me the couple times I tried it.
Good luck. But yea, start with what you already know is bad and plan to replace anyway.