Cu Chulainn
As part of the process for obtaining a FAA certificate based on your current EASA license, you will need to undertake a Flight Review to ensure that you are up to the standard required. There is also a related ground review so you should get the current FAR/AIM and study it.
Are you current on the R22? it seems odd that the place that you are renting from won't allow you to go solo.
Having a CFI with you will increase your $ costs quite substantially. You will also need to get it clear as to who is actually PIC. The CFI won't be wanting to be a passenger and not gaining any hours in his own logbook.