US community colleges (usually 2-year) tend to have low tuition and may offer flexible scheduling so you can pay as you go and/or work through school. Housing can still be expensive though.
US public universities may have lower fees for in-state students. UC Berkeley costs some $41K+ per year (including on-campus housing, food, etc.) for CA residents - not particularly affordable to begin with - but charges an extortionate $33K "nonresident tuition fee" on top of that for non-resident students (including any students under 24 whose parents live out of state.)
Public Universities are ones funded by the state, to varying degrees.
Private Unis have their own funding, usually through a mix of tuition and large endowments.