To get into deeper detail requires settling on one or more locations.
I think we can rule out any free-space colonies just on the basis of radiation shielding. The required mass is just so enormous that there does not seem to be any cost-effective way to collect it. A habitat for 10,000 people could take up to a few hundred thousand tons of shielding. NASA's asteroid retrieval mission was set to retrieve about one thousand tons for one to two billion dollars. Granted if one wanted to capture a hundred asteroids the economies of scale would drive down the cost, but we would still be talking about tens of billions of dollars.
Bodies with gravity are a decent idea. The Moon is close, fairly easy to leave (re-usable shuttles could be used) and a habitat there would have a useful level of gravity for plant, people and industry. The trouble is that the Moon has very little carbon, basically no nitrogen and an unknown amount of hydrogen in the form of water ice. Oxygen is abundant, as are lighter metals and silicon. As it goes, this might make a good stepping stone for proving hydroponic systems and resource extraction with less risk than some other places. Solar power on the Moon is hard because of the two-week night period; activity here will tend to run in cycles of two weeks busy, two weeks slow. A polar base could avoid that power difficulty in exchange for higher shipping costs. Because of the proximity to Earth, a Lunar surface base working with an L1 or L2 station could build or service satellites for use in Earth orbit; this is a near-term service with significant potential value. In the long run a Lunar colony would always require supplies from Earth or another colony, but will probably do enough business in trade to be viable.
Mars is another good idea. The gravity is higher than the Moon. There's carbon and buffer gases right there in the atmosphere, plus proven reserves of water ice and enormous amounts of iron oxides. All the elements necessary for plant life are available. Downsides are the harsh weather (nasty dust storms, sometimes for months at a time), long travel time (several months trip only once every 2.2 years) and high cost to launch from the surface to get anywhere else. As long as there is political will, some Earth governments might be willing to support a very basic Mars outpost. If this also includes the equipment necessary to produce PE plastic then that outpost could eventually produce the materials for the first large colony. Shipping costs are high and the travel time is long, so Earth-based launchers would probably be stiff competition.
Bodies without significant gravity are also possible. The Martian moons Phobos and Deimos are basically large asteroids in orbit around Mars. Solar power is more reliable than on the surface. There is no gravity to speak of, so shipping is cheaper. It makes the habitats more complex because they will need spin gravity, but there is still plenty of material to bury them under for shielding. As with the Moon there are no buffer gases, but carbon is available as is water ice. Ceres is another possibility out in the asteroid belt, with huge amounts of water but otherwise many of the same limitations as the Martian moons and the added difficulty of even less solar power available.
A Phobos base paired with a Mars surface base could be a very good team, particularly with the use of tethers. This provides reduced shipping costs, access to the full spectrum of necessary elements, a broader range of things for trade (including science data and samples in the early phases) and a nearby backup facility in case something goes wrong. That long gap between launch windows is still really annoying, but for bulk materials it could be managed. Martian surface exports would include structural plastic, argon for use in atmospheres and as electric engine fuel, nitrogen for atmospheres and as fertilizer, CO2 as a carbon source and methane as a fuel, carbon source and/or hydrogen source. Phobos exports would include water ice, metals, food, bulk shielding and valuable elements (platinum-group metals, rare earth elements, gold, etc.)
For now I will assume the Moon serves as a technical demonstration environment. Before technologies are incorporated into the final colony they will first be tested on the Moon or in Lunar orbit. That also means Lunar products will be available to accelerate the program compared to an all-Earth-launch baseline, and a market for goods and services in Earth orbit will exist. The baseline colony will be split between Phobos and Mars. My target is an estimated cost of $150 billion or less, roughly the cost of the international space station. As a permanent colony, the program can take a long time to complete if necessary but should result in habitable structures within 30 years.