Building a new block patio- How can I keep grass from growing back?

Apply a grass and weed killer and lay very heavy landscape fabric.

You will need to dig down at least 6" or three times the depth of the block. Lay landscape fabric down. Pour and tamp down 1/3 fine gravel then 1/3 sand. Lay your block. Pour sand over the block and sweep into the joints. Wet the block to settle the sand. Add more sadn an sweep into the joints again.

Read that sprinkling baking soda on bricvs will keep down weeds.

That's probably the best solution, but I'm trying to avoid having to have a yard of gravel and a yard of sand hauled in. Thanks.

You need to create a weed/grass barrier around the edge of the patio. Heavy landscape cloth will work well. Fold it up so it cover the edge of the pavers. You need a good compacted gravel and sand base as mentioned above to stop the patio from shifting and make sure it drains properly. The other important thing is use a sand that is not 'friendly' to grass or weeds as both the base sand and the sand between the bricks. It's referred to as paver sand.