There are several avenues for startups to connect with designers. Platforms are dedicated exclusively for design professionals - enviro, theme forest, oDesk to name a few. Depending on your project & size you get work done for a reasonable price.

As long as your are cash strapped, I would reserve equity for employees. Equity serves as a great incentive to grow your company in the years to come.
With that said, I know of tech/dev companies that partner with startups to work for equity until they can be paid at a future time