Starting out, looking for someone to look over a pre-approval plz

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Hey BP community,

Just getting started getting out of this rat race we call life (finally!). Been doing a ton of reading and research the past few months and getting ready to take the plunge.

Got my first pre-approval and I have a sneaky suspicion that they offered me a terrible rate, knowing how new I am. I understand that I won't qualify for a killer deal my first go around and I am not expecting to. I just would like to know if I will be wasting time to save a few dollars by shopping around or if it is really worth it to bring my business elsewhere.

I have great credit (750+) and enough money in the bank to do this deal in cash, if that makes a difference.

Thank you so, so much for your time!

Details:

Purchase price: $50,000

Loan amount: $40,000

Down payment: $10,000

Interest rate: 6%

APR: 6.404%

TIP: 116.332%

Monthly principal and interest: $239.82/month

Estimated Taxes, insurance and assessments: $292/month

Estimated total monthly payment: $532

Estimated closing costs: $8,247 (+$10,000 down payment)

Breakdown:

Origination charges: $950

Appraisal and all title fees: $1,862

Recording and transfer taxes: $800

Prepaid homeowners insurance and interest: $697

Initial escrow (2X months Homeowners insurance + 12X months $250 property taxes): $3,000

Other (buyers personal attorney fee $450 + Title-owners Title Ins $405): $855

Thanks again so much for your time and input.