The interest rate does tie in with your score for conventional loans, not so much for government insured loans (like FHA).
Also, the higher your score, the lower your PMI rate will be - and that is huge if you aren't putting down 20% on the purchase. With conventional loans and a LTV above 80% you have to qualify for both the loan itself and PMI.
There is a significant difference in PMI rate if your mid score is 720 or above. The best rate for PMI is for borrowers at 760 or above (mid score). Here is a chart for one of the PMI companies (there are only a few in the country) https://www.mgic.com/rates/rate-cards.html
From where you are right now, 720 could be very achieveable quickly. And the difference between the rate at 720 and 760 is relatively small, but the rate for less than 720 is substantial. Take a look at the link for borrower paid MI fees - paid monthly. There are different types of MI you might want to explore too- for example Lender Paid MI, but your interest rate increases if the lender pays for your MI.
If you are putting down 20%, then the PMI doesn't matter because there is no MI charged 
You are considered a first time home buyer (again) if you have not owned property for 3 years or more. The clock starts from the date you transferred the deed to the new buyer. I know this is true for Fannie, Freddie and FHA. I don't know anything about the Section 184 loan or USDA. I suspect USDA follows FHA standards, but I don't know for sure.
Back to your original post: if you are going FHA you don't need to do anything with your score, you are fine The MIP (mortgage insurance premium) for an FHA loan is charged in two ways: the UFMIP (Up Front MIP) paid at closing and usually rolled up into your loan (you can pay it at closing if you want but you have to request it) and the monthly fee which is 0.85 basis pts of the amount borrowed. eg, if you borrow $100k (as an example, your monthly MIP will be $70.83). The UFMIP for FHA is 1.75%. These MIP rates for FHA are automatic and you only have to go through mortgage approval. If you are approved for an FHA loan, you are automatically charged this rate. It does not fluctuate with your credit scores.
WOW, consider myself put in my place 
@ezdriver wrote:
@Anonymous wrote:I asked my potential lender what credit socre was needed to reach the next level for a better interest rate. She started double talking about how she can't tel lme that because it is different for everyone. My mid mortgage score is 710 and I wanted to know what score I should aim for but she wouldn't answer that. She just did a bunch of double talk about down payment, etc affecting the interest rate so there was no answer to that question. Is she right, or should I just skip the bank completely? I won't let her do a hard pull or file a loan app until I know I am where I need to be DTI wise. I want a loan in the $180,000 range.
I'd like to comment on a couple of thinsg in your post.
1) Please understand that a loan officer quotes from a "rate sheet" which is a matrix-type document. On that rate sheet are many factors one must select in order to provide an accurate mortgage rate for a specific loan scenario. What you perceive as "double talk" is her way of providing general information to you while you in turn are looking for specific information ... which brings me to point #2.
2) No one can give you an accurate rate quote without having had an opportunity to collect and review a lot of documents ... starting with your credit report. To expect anyone to give you a meaningful rate quote without the credit report at a minimum is silly.
3) Personally, I consider all rate quotes to be meaningless until a borrower can lock a rate. It takes a lot to get to that point.
I'm just sayin....
I'm nowhere close to an expert but if a lender won't let me look off the rate adjustment sheet they're using (I can read the Fannie Pricing Adjustment guide as well as they can IMO) I'd consider finding another one.
Yup, it doesn't mean squat until the rate is locked, but the pricing adjustment sheets that the individual lender works off of should be available if I request... some even post them online. Sure the difference in my rate between now and the end of the year could be 3.75 vs. 4.0 (for the sake of the argument), but if I know I'm going to be at 4.0 now because I put less than 25.1% down (and this was true for all conforming conventional mortgages for condos I could find and it's straight off the Fannie worksheets) why not at least give me the chance to optimize my financial situation and make the informed tradeoff between DP and rate? There's one too for 700 vs. 720 as well in Fannie land too for that matter that I was running up against (and hence my being bouncing off the walls happy at clearing 720 on my trifecta mid score).
Could give other examples just from my discussion with Chase today even, mortgage rates are more than just FICO score even though that dictates where you get slotted into for the matrix, it's still a multivariable equation when it comes to determining rate, and I'd be willing to bet the pricing adjustments don't change all that often: they certainly don't for Fannie / Freddie.
Why would a lender not disclose their pricing breakpoints to me unless they were trying to be, well I'll charitably call it opaque? No thanks, be transparent or I will find a lender that will be... thousands of mortgage lenders out there and I only need 1.
Possible the right question didn't get asked but if my LO is vacillating over this, what is to suggest anything would be different in the future? I'm a somewhat informed consumer, at least let me make an informed decision.
