B2N2 makes a good point - in the US there are two ways to get a licence, part 61 and part 141. Because part 141 is taught to a specific approved course, they can be done in fewer hours (35 for PPL I think) and the IR can be done sooner. Doing it all in the same aircraft is also a good point, but to be honest switching types of not a massive problem, and the is plenty of hour building to be done. Logging the EASA way is also a good point (In fact two logbooks would make life easier) If you intend to get CFI work in the states, this is a great plan. However, if the plan is to get an EASA CPL MEIR and work in Europe, it's a bad idea..
To get an EASA CPL requires 200 hours. To get an FAA CPL requires 250 hours, and you still have to convert it! To convert an FAA CPL to an EASA CPL would be 15 hours, and to convert an FAA IR to an EASA IR would be 15 hours, so you're looking at 280 hours total.
Basically the cheapest way would be FAA PPL, FAA IR, hour building, FAA multi (to finish with 170 hours, 100 PIC) then EASA MEIR & EASA CPL single: 200 total