Lending guidelines are very different. Also, no one provides a Letter of Commitment without a specific property address. Did you mean a pre-approval letter?
If you have a letter of prequalification, or preferably approval, you should be ready to start looking.
You asked about HUD and your letter should be fine, but keep in mind that HUD gives preference to owner occupants, meaning that they will only look at offers from investors if they don't receive an acceptable offer from someone who plans to live in one of the units. There are many other properties available that do not have these requirements.
You may find the search page below useful... it has an option to search specifically for residential income properties.
Robert and Dawn