Chances are pretty good the motor is sticky from old oil & dust accumulation. Easy enough to clean with DeOxit then lubricate with a light oil. Needle Doctor and similar retailers carry oils, belts, cleaners and other parts. After that's done, check the speed again to make sure it's stable. Something else could be going on otherwise.
Isolation feet may or may not be necessary depending on where you locate the table, how rigid your floor is and other factors. I suggest you start with a sorbothane patter mat. Inexpensive and an easy way to isolate noise. Use it in place of the stock mat.
If the headshell isn't bent or dented, don't worry about it for now. The cartridge is probably toast if it's original. The magnet weakens over time. Go with an Ortofon 2M Red or similar - reliable, inexpensive and performs above it's price point. Make sure to take the time to align it properly with a good protractor and set the tracking weight at 1.8 to 2.0 grams. Replace the cartridge leads, too.
I found the Pro-Ject Strobe-It to be a useful tool. Has a strobe on one side and a very easy-to-use protractor on the other. Patience is the key to getting everything working properly with these old tables and is well-rewarded.
Good luck & happy listening!