1000GPH gives around 16gpm. Water carrying ability of hose/pipe is a matter of both size (1/2", 5/8", etc), flow you're trying to move, and length. If you use a hose that is too small, you will lose a lot of your flow/pressure to friction losses in the hose, and the longer the hose is, the more dramatic the effect will be.

1/2" hose is out, it has a very low flow rate. 5/8" is probably acceptable as long as you only run a normal small lawn sprinkler and stay under about 100' length. If you want to run longer hoses, or run a large sprinkler, you will need 3/4" hoses.

Check out stuff like https://www.bigsprinkler.com/catalog/sprinkler-heads to see some options that go beyond what will be sold at your local hardware store. For example, one of these https://www.bigsprinkler.com/catalog/sprinkler-heads/impact-sprinklers/jumbo-sprinkler will need a full 3/4" hose, but will cover up to 100' diameter at once.

For a more basic option, something like the Gilmour tripod sprinkler https://www.amazon.com/Gilmour-819003-1001-Adjustable-Circular-Sprinkler/dp/B0036G2OZO/ has impressive range and usually only needs a basic 5/8" hose to supply.