How many total judge positions are there, that are nominated by the President?
I think the total breaks down like this:
9 SCOTUS judges
There are 179 Circuit Court judges.
There are 678 Active District Court Judge positions.
These are totals. Obviously no president is going to get to appoint the entire judiciary. IMO, it’s the SCOTUS and Circuit Court judges who are really important. The Circuit Courts heat a lot of cases that never reach the SCOTUS. That makes them really important from a practical standpoint. District Court judges can always be overruled if they issue a bad ruling but there are a really limited number of cases the SCOTUS can rule on.