The Moon is nice and relatively close and a good place to learn to be self sufficient.
Technologies like 3D printing hold enormous promise... you could have machines that grind up moon dust and moon rock that can be used to make shelters from local materials... some sort of polymer or other material that binds it up and makes it solid like rock with an outer covering in case of any dust storms or incoming material from the sky.
Boring machines could dig tunnels deeper under the rock and the spoils could be used for above ground structures where needed for even better protection from solar and space radiation and solid matter like meteoroids.
Operations on Mars will be easier despite the much greater distances because assuming some sort of reliable power source there is atmosphere and material for various things too... actually mining Mars would be cheaper and easier than mining the asteroids because the asteroids are so far away and so far apart... if asteroid fields looked like the ones in movies and documentaries the distance out from the sun would mean there is more material than in all the planets combined to create a ring that wide and deep around the sun.
The real asteroid belt standing on a decent sized asteroid... and there are some big ones.... you would not be able to see any other asteroid in the field... they would be too small and too far away... if they were as dense as the asteroid belts shown in Star Wars they would have collapsed together and formed planets with that much matter and those planets would be huge.
Getting a manned station on the moon would be a good first step and the technology needed to operate self sufficiently without every little thing needing to be sent up and brought back would be good experience for longer trips of greater distance.
If it worked I would say a long range remote control mission with a space tug to one of Jupiters or Saturns moons would be an interesting experiment too... testing instruments in extreme gravity and radiation fields would be valuable and returning it to earth orbit so it can attach to ROC and be examined and tested for damage and fatigue would be a useful base of information for future missions to those far away places.
The increased flight speed should shorten flight times and make even return trips from Pluto and Charon and perhaps even objects in the ort cloud would be possible.