Hi Jackie,
I'm not a conventional lender but was one for 30+ years here in South Florida. The closing costs seem in line with a typical transaction assuming the property is located in Florida. Here's why:
The State has 2 taxes they charge on mortgage loans. The 1st is Intangible Tax which is .002 x the loan amount and the second is simply called a Mortgage Tax. This is calculated by multiplying the loan amount x .0035. In your case these come to $1,650. Recording fees at the county will add another $250 or so depending on which county the property lies in.
Title insurance on the mortgage will be based on the lender's coverage requirement of $300,000 to cover the note. The cost of insurance, document prep, lien searches, settlement fee, etc will cost you roughly $2,500 depending upon the company you choose to close with.
Your lender will want an appraisal of the property. Typical cost for a residential appraisal is $450-$600. Depending upon the interest rate you choose points may be charged to you. For example, If you were to choose a hypothetical rate of 4.25% for a 30 year fixed you may have to pay an origination fee of 1% or so (loan amount x 1% = $3,000 in your case). If you choose a higher rate you may not have to pay points but the long term trade off in higher payment may not be worth it. Your anticipated length of ownership will dictate which way to go on this.
Beyond points lenders also charge ancillary or 'junk' fees. You'll see terms like 'underwriting fee' or 'document prep'. These fees can easily reach $1,000 per deal.
So to recap, the closing costs on a $300,000 conventional mortgage in Florida with the lender charging 1 point will come to approximately $9,000 which comes out to 3% of your loan amount.
Hope this helps clarify for you.