If you already have 45 hours and a PPL, i would do the odd hour here and there upto when you start your ATPL. Get your ATPLs out of the way first as there is no certainty that you are going to pass (although im sure you will) which would make the hour building a waste of money.
Then go to the states, do your hour building, then your going to be very prepared to do your CPL and FI(R).
If you do the hour building first then take a 7 month break from flying to do the ATPLs, your going to be rusty and may need some hours just to get back up to scratch.
My advice......
ATPLs
CPL
FI(R) or IR (in any order)
Good Luck
