While there are some assistance programs for first time home buyers, there really isn't a specific loan program. You will get either a conventional or government loan. If you're looking for something with no downpayment, it would have to be either a VA loan, or and FHA loan through Utah Housing Corp (which is a downpayment assistance program). With 3.5% down you can get an FHA loan, and with 5% down you can get a Conventional. USDA rural loans are also no downpayment loans, but Salt Lake will not be eligible - you will need to look for a property in an eligible rural area.
You can read more about different loan programs on my website, and contact me with your questions.