"Close" means a different thing in Space than it does on Earth.
If the planets are aligned the Delta-V is not that different between the two (Mars is about twice as much Delta-V for 100x the distance). You can use aerobraking in the Mars atmosphere but can do no such thing on the Moon. And then the last problem is that on the Moon you need to budget for a round trip, but on Mars we could produce fuel on the surface for the return trip. When you start thinking about all that it's obvious that Mars makes more sense.
Can we actually? And I mean in any reasonable time frame say 100 years? And by self-sustaining I take fully independent from Earth supply chain for absolutely everything. A civilization that could continue existing without single delivery for Earth.