If you are the first time home buyer, some banks do offer incentive programs for first time home buyer. Basically, the program would give you free closing cost, and/or some discounts on the second loan (if you cannot pay up to 20% down payment). As I know, at least Citi and bank of America offer that. Check it out.

For the interest rate, I just got quote from Citi and bank of America yesterday. 30 years fixed is around 5.825% to 6%, 7 years arm 5.5% - 5.75%. It may depend on the location and how much you are going to loan. I am 30 minutes north of NYC, and looking for 250K to 280K loan.

I guess if the bank offers you higher rate, you should be able to negotiate the closing cost.

Just my two cent, hope it can help, good luck!