Folks jump to the presidency, but seems like the biggest value prop for a third party is winning a few Senate seats. Target 10 smaller, purple states with one major media market. 2-3 wins in one year gives six years to build momentum.
With each added Senate seat in subsequent years, the third party builds relevance by setting the Senate agenda. Given how evenly split the country is, just a few Senate seats have outsized influence. House is possible too, but with only 2 year terms, the value is harder to maintain and build upon.