There is no single answer to your question because each lender have their own guidelines. With respect to FHA, one lender may be OK with (1) open tradeline but require you to provide alternative credit info such as verification of 12 months rent paid on time along with a utility / phone bill etc. Another may want to see (3) open tradelines for at least 12 months.
Since the rules will vary between lenders, you should meet with a mortgage broker who has many lenders so they can find the best one for your situation. You should also get advice from them how to increase your FICO's. A higher qualifying FICO score will = lower interest rate and will save to tons of money over the life of a loan.
All the Best!,
To answer your question 623 is not a great credit score and lenders generally look at three credit lines. Now, as the gent below quickly jumped too credit score will drive which programs you qualify for and what rate you get. Yes, with FHA you can still qualify, but your rate may be a .5 point to a 1 point higher then somebody with perfect credit. If you want you can ask the seller to contribute up to 6% back towards closing cost and you can use that money to buy points and get the rate down. I would really only recommend this if you plan to stay long or if the 100 bucks a month is a huge savings to YOU. Best