With the exception of condos, where the association has to be already approved by FHA based on owner-occupant levels, any home can potentially be purchased with an FHA loan.
Most loans in the last 10 years have been FHA, and if it weren't for the FHA program most people would not have been able to buy homes after the real estate bubble popped. With FHA, you only have to come up with 3.5% for a down payment, instead of 20% for a conventional loan. There are income qualifications that buyers have to meet, but it's very reasonable.
As far as the home itself qualifying, your lender will have to send an appraiser out for their purposes, but FHA will also send out THEIR appraiser/inspector too. The house must appraise for at least the sales price AND everything in the house that is supposed to work, must work for the FHA inspection to clear. Ex: all appliances must work, plumbing must work, electrical must work and be installed properly (outlets and lights grounded), windows must be operational. My experience has been that an FHA inspection is not as thorough as the buyer's home inspection, but even if there are things that pop up, the seller should fix them so the deal can go through.