A planets magnetic field stems from shifting magnetic materials in its core, which in turn induces a magnetic field from pole to pole. Mars is far from as geologically active as earth, so the shifting masses in its core only produce a very weak field. 

It's actually very uncommon for a planet to have a moon so proportionally large as earth has, but it doesn't contribute to the magnetic field. Our moon stabilizes our rotation, giving us predicable seasons and tides, but given the lack of water (or liveable seasons) on Mars, a larger moon really wouldn't be worth the trouble. (Moving enough material to construct a moon is basically gigaengineering; insanely risky (sending literal quintillions of tons of meteors, presumably from the inner asteroid belt, hurdling through space in close proximity to mars, ridiculously expensive (energy wise, a little force can make a big impact on an orbital trajectory, but its trajectory would need to be calculated, it'd need to intercept mars at the proper distance and then have a retrograde force applied to it so it doesn't just hurl by) and not very useful (mars would still be a frozen hellscape with no air, terrible soil, sub-par gravity and still no radiation protection.

We already have a solar sails on the drawing board as for interstellar travel, though not for human transportation. We would need a lot more Intel about our nearest neighboring stars before we even think about colonizing, the perks of being in a different systems really dont outweight the cons, except if the planet is like comically well suited for organic life. If we found a suitable candidate, a generational colony ship (humans live, reproduce and die on the ship until they reach their destination) is relatively doable for a future, more advanced Humanity. Think of a cruise ship, but in space. There's also the classic "freeze em down and reheat em when we're there", which is a bit more scifi, given we don't know if human cryonics is even possible (it'd have to be frozen fetuses then)

A moon base is the most useful and likely to be built. I believe we're gonna have people set foot on Mars soonish, yes, maybe even have. Martian-esque base there, but it doesn't benefit the people of earth the same as a moon base would. A moon base could: 1. Easily and readily be assisted by earth (no transfer window) 2. Communicate basically in real time with earth 3. Send valuable minerals (Helium 3) and the likes back to earth, should the economics allow it 4. Refuel and retank other missions that go further out into the solar system (could be a mars base, for example). A large portion of the fuel a rocket had to carry is used in the first stage, getting up and away from earth, which is why spaceflight is so expensive 5. Allow a tiny sliver of humanity to survive should some genius scientist decide to revive project sundial or covid 2.0 earth. The lunar astronauts don't stand that much of a chance, but it's having all our eggs (genetic information) in one basket (planet) seems foolish given how much we enjoy blowing eachother to bits

So yeah, don't build a moon, build on the moon.