1) Should I get Lee 3 die sets, or 4 die sets?
Up to you. They will both do the job, but the 4-die sets are easier to set up and allow a bit more flexibility in how much crimp you apply to the revolver rounds.
2) I suppose the die set answer to question 1, will determine whether I get the 3 or 4 hole turret press?
I don't think Lee sells the 3-hole turret press any more. You might want to check. In any event, I suggest the Classic Turret (which ONLY comes in the 4-hole version) because of the way it handles spend primers and its overall strength. It is cast iron. The Deluxe is aluminum.
The 4-die turret will operate just fine with a 3-die set. One die station will be empty.
3) I assume .38 Special dies will work for .357 magnum also?
Yes, but there are a few dies sets floating around in which the .357 mag crimp/seat die is too long to do the 38 special. I am not sure about the case-mouth belling die.
4) If the answer to question 3 is yes, then may I assume the same turret will work for both?
One of the reasons for having multiple turrets for multiple calibers is so you don't have to re-set the dies when switching. Though you can (in most cases) use the same dies for both 357 and .38, all but one of the dies (the exception is the sizing/decapping die) have to be adjusted differently for the two cartridges.
5) Will the same diameter bullets work in .38 Special and .357 Magnum?
.355" for 9mm (.356" in lead) .357" in .357 and .38 and .358" for lead bullets in .357 and .38. Different guns may cause the ideal dimensions to vary a bit.
If you use .355 bullets in a .357 diameter barrel, the bullet may not fill the bore and allow some gasses to pass the bullet. This will cause leading if the bullet is lead and may cause some erosion of the bore.
Because the power levels are greater, the .357s are often constructed a bit tougher than bullets intended for 38s. But the dimensions are identical.
6) Is Unique powder suitable for working with 9mm, .38 Special and .357?
Yes. Unique is good for 9mm and 38 and for lightly loaded .357. For heavy .357, a slower powder will produce the desired energy with lower peak pressures. Study up on interior ballistics, concentrating on powder quickness.
Some say Unique is sooty (they call it "dirty") and hard to meter. I have not found it particularly difficult to meter and gun cleaning is an edifying post-range ritual, in my opinion.
I have no experience, sorry.
8) Will the same primers work for 9mm, .38 and .357?
Yes, All three cartridges take small pistol primers.
No, Depending on powder (and power level), standard or magnum will work better than the other.
Good luck.
Lost Sheep