You are not limited to any type of house (although condo ownership can be a problem with FHA financing) but you are limited to "houses without major problems or safety issue".
A cash buyer can purchase any home.
A 20% down conventional home purchase may require repairs if any major defects are known or discovered by the appraiser. The bank may not lend the money to purchase unless these repairs are done before closing.
With an FHA mortgage, you are required to put a minimum of 3.5% down. When the appraiser goes out to the property they check for repair issues PLUS safety violations. If the house has flaked paint and it was built before 1978 they may require scraping and painting (it could have lead).
The "mortgage required" repairs and safety issues can usually be negotiated with the seller IF the property isn't being sold as-is (foreclosure and short sales are usually as-is).
The differences in financing (cash, 20% down, FHA) can determine negotiation power. A cash buyer has more negotiation power than an FHA buyer. A seller may accept an FHA offer but state they are not going to do any of the FHA required repairs. There are cases where the buyer has been painting their future home in order to satisfy the FHA flaked paint condition.
A work around for repair or safety items is to do an FHA 203k Renovation loan. You borrow the money to purchase the home and on top of that borrow the money needed to repair or upgrade the home. This loan has a higher interest rate and will change your purchasing power.
Hope this is of some help.
Prudential Patt White Real Estate
Lehigh Valley, PA
Cindy Vedder. Prudential ca. Realty
Good luck, and if you need any assistance, call us at: (888) 9-List-It. That's (888) 954-7848.
Best of luck...