First time loan recommendations? - Nashville, TN

Hey there! I need help!

I'm a first time buyer (Nashville, TN) looking at financing and wanted to get some unbiased input! I've got about 12k in reserves, good credit, and a steady job. I'm getting ready to do my first deal and I was hoping someone could recommend some good numbers to look for in a first time loan? (please excuse any ignorance :)) I'm hoping to do an FHA (3.5% down) possibly with a 203k if it needs repairs. I will be living in the property at least for the first year.

These are the rough numbers I am expecting right now :

Loan amount: 180k

Down payment: 3.5%

Interest rate: 3.734%

type: 30 year fixed

PMI: 1,702/year ( .9%)

Some questions I have: 

- Is this a good loan for a first time investment property?

- What do I do if my lender comes back and says the best they can do is a much higher interest rate? 

- Will it hurt me (credit, reputation) to "shop" different banks and lenders?

- Is there anything I can do to not be "tied" to the PMI?

- Should I let the lender provide the Home Owners Insurance, or should I seek out a policy myself, or does it not matter?

I don't want to be impossible with my expectations but I also don't want to sign onto a bad loan. Sometimes I feel like loan officers can't really offer truly "unbiased" advice. hmmm . I'm going to be doing a couple of meetings soon and just wanted to come prepared:)

Any input is appreciated SO much!

Many thanks,

Sam