Caring for those who cannot care for themselves. Law enforcement and prisons. Health care. Education at a basic level, although there is a place for private higher education. Soldiers. Regulatory enforcement. Administration of public lands (I oppose contracting out services at Nat'l Forests). Disaster relief, first responders.
Contract supervision for things we can only do collectively, such as infrastructure, defense, basic research, and yes, there is room for the arts.
Plenty of room for capitalist enterprises, I believe strongly in that. I look around me and see many things I purchased from for-profit businesses, my house, truck, RV, motorcycles, this computer, my Gag Factors, food, dog meds. I was part of the military-industrial complex, working for companies that got Gov't contracts to develop weapons systems. Scientists and engineers, not mercenaries.
Of course, neither of these are all-inclusive lists.