On any type of car diagnosis/repair, start with the easiest and cheapest first.
On the transmission, you do not say how many miles or what kind of previous maintenance. I would recommend starting by changing the manual transmission oil. Pull the filler plug first, and then drain and save the old fluid. I think it uses a 14mm Allen wrench (double-check this). Look at the old oil. Is it dirty? Are there metal pieces or filings?
Refill with synthetic fluid. I use Redline MTL, but there are numerous others available. Replace the washers for the drain plugs (if equipped). Drive your car and see if anything improved or changed. If the transmission is bad internally, it will normally make a grinding noise, rather than a squealing noise.
Your clutch release (throwout) bearing will need to be replaced soon if it is making noise. The squealing could be from the release bearing too, or it could be the pilot bushing. You will want to replace all during your upcoming clutch job.
If your car has some miles, the control arm bushings should be replaced. This is a designed wear part. They are relatively inexpensive. But, I am not sure if this will cure your shaking. Look at tire balance, tire out-of-round, etc.
:drive: