Is the house you thinking about buying for you and your fiancé a duplex or triplex? Funny; for me I want to house hack before even considering buying a non-occupied investment property. In your situation, seems like you have the ability to buy a non-occupied rental. If the numbers are right and the house you and your fiancé want to live in isn't a multi, imho I would lean towards the non-occupied rental.
I am going to buy a rental before buying a home for my family. We get a pretty good deal on our rent ($1275) and we like not being tied down to this area (Seattle). Plus the market is very hot here and we don't get to find a screaming deal because everything is flying off the shelf.
Do you have the option of buying a multi-family in your price range and living in one side while renting the other?
Do you have additional savings to cover repairs and problems that may arise in your rental?
Are you saving up money each month at your current rent rate? How long until you could save up enough to buy the $110k property if you did purchase?