Yes, you are correct. The granters tax is typically paid by the seller and is $1.00 per every thousand. On the purchase of new construction (as Nancy said), they typically make the buyer pay grantors tax. As a buyer your costs associated with buying a home would be "closing costs". I tell my clients to expect a total upwards of 3% of the sales price toward closing costs. I would be happy to review a HUD 1(a settlement statement showing a breakdown of all your costs) with you.
Below is a basic overview of fees associated with purchasing a property that would total approximately 3%.
Lender associated fees: loan origination fees, points, appraisal fees, credit report, flood certification, mortgage insurance premium and homeowners insurance.
Government: city, state, local taxes, recording fees and grantors tax.
Settlement fees: title insurance (owners and lenders), settlement fee, release fee, document fee and attorney fees.
Give me a buzz when you would like to review in detail.