What is valuable in the belt?
The big reason to go to the asteroid belt is to get valuable materials. I believe that the most valuable materials to be found are volitile compounds such as water, nitrogen-rich ammonia, carbon dioxide, or methane. These things are not strictly abundant on Mars, and you may want more of them. Especially if you are making a biosphere via terraforming, you will likely want a lot of ammonia to process into nitrogen for an atmosphere, carbon dioxide to process into oxygen, and water.
The amount of metals or other minerals that industry would demand would be insignificant compared to the amount of materials needed for terraforming. While some metals are very valuable, if you did mine a lot of those metals, prices would drop and might make them less profitable. Demand for rare metals just isn't that high right now compared to the amount available on Earth, the Moon, or Mars. Regarding volitiles, if space based colonies around Earth or elsewhere in the inner solar system are a thing, they may have demand for ammonia (for fertilizer), water, and carbon dioxide as an oxygen pre-cursor. This could produce high demand, even if there is not the very large demand from terraforming Mars.
How many people would have to live there?
Given that you want those materials, it would be best to mine them and process them into frozen balls, then shoot them towards a Mars orbit where they would be captured and processed as desired. The closest place to Mars to get such materials would be the asteroid belt. Farther away locations, like the moon systems of the gas giants, might have better sources of materials (i.e. more concentrated, especially for methane), but transport costs will be higher due to distance and the gravity wells of those planets.
Thus, you will want industrial facilities in the asteroid belt to process materials for shipment to Mars. Here is where automation matters. Some would argue that these facilities could be completely autonomous. I think that is pretty optimistic. I believe that there will have to be stations of maintenance personnel to manage these industrial stations where asteroids are broken up, separated to release valuable elements, re-packaged, and then transported off. There is a lot going on with these processes, and equipment breaks. You don't want to have to launch from Mars (potentially years away) to fix problems in the belt.
Furthermore, I don't think that completely autonomous vehicles doing the mining/crushing/packing is realistic either. I think they will be partially automated with human 'operators' controlling them; the way drones are operated today, or like the construction equipment is pictured in Avatar. If that is the case, you certainly won't be able to control the vehicles remotely from Mars. The lag time for signals would be several minutes. In that case, you will need even more personnel living in the asteroid belt as remote asteroid crusher drone operators.
Once you have a working population of thousands, it becomes efficient to have some 'cities' or stations that serve as commerce and entertainment hubs for the workers in the belt. Again, the distances involved in taking leave back on Mars, much less Earth, are prohibitive.
There is no reason to concentrate these people on Ceres. Ceres' surface gravity is 3% of Earth's, not enough to provide any medical benefits for humans living there. Humans would be much better off living in larg space habitats that can rotate to create their own gravity. Some planets or large moons might not have enough gravity to support humans, but would still be valuable for agriculture. Mars is most likely to fit this criteria. Ceres' low gravity would probably preclude even genetically engineered plants from operating properly (regarding internal water transport, specfically) even if kept in pressurized greenhouses. Ceres' low insolation doesn't help. Even farming for these residents of the belt is best done in space stations.
Living in the belt just to live there probably isn't great
There isn't a lot of motivation to live in the belt if you are not either working there, or operating a business or service for those working there. There is a lot better real estate in the solar system for things like space-based farms and solar energy. If you were going to have space colonies, then you would want them much closer to the Sun, perhaps even closer than Earth, to take advantage of food production and cheap energy.
Thus, your overall population would be low, just enough to support the industry. This would be much like mill towns of the Industrial revolution, like Lowell, MA or Blackburn in the UK.
The materials most likely to be in high demand are volitiles like water, carbon dioxide, ammonia, and methane. If this demand is high enough, the asteroid belt is one of the best places to meet this demand for the inner solar system. Unless you believe that the industry for refining and shipping these materials will be fully automated, you could expect the asteroid belt to be littered with 'mill towns,' clusters of space stations and space farms that support the operators and maintenance techs of the asteroid belt industry.