u/Ambitious-Mood5161

So I’m a little confused when it comes to loan types and shopping around. To preface, we are first time home buyers and in our mid-late 20s so please be easy on us. So we just got our first preapproval- my fiancé’s credit score is 640. He only has 1 credit card that’s barely used, has $30k student loans, and currently makes $110k. My score is 718 and have 3 cards used often and always paid off on time, no loans or debts, and currently makes $138k. The lender told us to go FHA due to scores and said he can do conventional but it seems like FHA might be better for now bc the interest rate will be lower. My question is what can we do in the next few months (6 months) to get it to a good point for conventional rate and what is a good conventional rate? Should we still look around? Should I drop my fiance and just use my score and income to get a better rate? We plan on putting 10% down payment and in the NJ market so hoping to get a house in the $500-600k range. TIA!