I am unemployed and receiving UI this year, but my income is low enough to qualify for Medicaid and I live in an expansion state. Can I choose between that and marketplace subsidies?

No.  If you are eligible for Medicaid you cannot be eligible for marketplace subsidies.  Some people who receive UI benefits will be eligible for Medicaid, in part because Medicaid will NOT take into account the $300 per week federal supplemental UI benefits.  When you apply through the marketplace, you will receive a determination indicating whether you are eligible for Medicaid. 

Medicaid coverage is also free or low cost (some states charge a nominal monthly premium for some adults) and requires no or only nominal cost sharing for covered benefits.