There are several kinds of colony...
- Some are nothing more than a place to house a military or commerce base. Adak, WW II Guam, WWII Solomon Islands, Dutch Harbor.
- Some are places to preserve a culture Ambler, modern Solomons, many of the polynesian atolls, Isle of Man.
- Some are places to extract resources from the environment. Juneau, Kuparik.
- Some are places to disappear people to. 1700's Australia and Guyana.
- Some are population density reduction. (This isn't the same as a place to send the disaffected.) Much of the American West in the late 1800's, the american east in the late 1700's, Australia in the mid 1800's.
- Others are to destroy an indigenous culture. Barrow, Sitka and Kodiak in the mid-late 1800s; every US Native American Agency pre 1930; Eastern Siberia.
- Others are to exploit indigenous peoples labor. British Raj, Spanish Cuba, US Hawaii in the late 1800's, Japan's "South East Asia Co-Prosperity Sphere" (ww II), Nazi Africa, Nazi occupied greece and turkey, pretty much any soviet-era "-stan SSR", Ukraine from about 1850-1996.
- Entertainment is the purpose for some colonies. 1900-1930's Cuba was mostly about entertainment; modern Kauai and Maui, modern Orlando.
Cultural preserves and cultural eliminations are often outside supported. Art and luxury resources often are able to bring about a significant improvement in local economies, but as a rule, they are funded.
Resource extraction is often self-supporting while the resource lasts. Juneau could support 1000-2000 people based upon its jade and gold mines. It's 30-40 thousand are mostly supported by working in government; it pays its own way as an administrative center; even if the state gov't dried up tomorrow, Juneau would continue to exist for another 30-50 years... the expected lifespan of the gold and jade mines. Logging would become more important, too - it could support another 2-3K people based upon fishing and logging. The goods would pay well enough to import what can't be locally grown, harvested, or manufactured. Eventually, it would become a group of several fishing and logging towns, as the mines ran out, and people moved into remote areas to log them, too.
Entertainment colonies are, at present, mostly about tourist getaways to unusually stable climate naked-body survivable locations. They are often self supporting when the tourists aren't there, but during their tourist seasons, the overall community is importing massively - tourists, money, and the goods to feed the tourists. These are the kind most likely to have all the conveniences and luxuries.
Creation of new cultures is often supported by some group back home, and are the most likely to be in for the long haul... and to fail spectacularly. The exceptions are so notable that they're mythologized: Deseret (Mormon cultural colony), Plymouth (pilgrim culture), Prester John's Kingdom (Probably Eritrea), Moorish Al-Andalus, Mount Athos. Note: All of these were religious in origin; all were initially supported from outside, and Mount Athos still is; all became self-supporting. The failures are equally as interesting: Jonestown (Guyana), the various Shaker communities (to be expected - they swear off sex, even within marriage), the Rajneeshi commune in Oregon, several compounds founded by members of Rev. Sun Myung Moon's "Unification Church", several FLDS compounds, Branch Davidians, literally dozens of separatist groups in the early 1800s. The failures are of two broad brushes: unable to sustain themselves when the outside help dries up, or run afoul of the nearest neighbors due to clash of cultures (including being in the way of the parent culture they were trying to escape from). Ironically, Juneau is just south of one such enclave - A Russian Orthodox monastery from before Juneau became a town - was occupied for some years; it eventually failed, but the buildings are still in place.... and maintained by the state, as it's in a state park. THey can be rented from the state parks department for special occasions.
Places to reduce population density are often initially subsidized, as well. Most of the US east Coast was used this way - the subsidizers were the colonial organizers in many cases - wealthy, and wanting to stay that way, they paid for others to come with and work for them on indentures.
Places to send the undesirable are different - they're often maintained in two tiers - tier one are paid to keep the members of tier two in place, and tier two are expected to support themselves in place, no matter what. Some are penal colonies, some are ethnic dumping grounds, some are political dumping grounds. The haves are usually well off, and supported almost entirely by the homeland.
Most current colonial enterprises are either religious separatists, political separatists, resource extraction, or cultural preservation.