List of Mission Types your character/crew may be interested in

I will include some descriptions at a later time

1.) Mercenary Work: working as a hired soldier. In general, mercenaries are fairly well respected in the Gemini, since they are essentially the equivalent of the armed forces for everyone other than the Aeneans. Mercenary work is very high risk, but the pay is decent and the difficulty of the work is typically low. Also, significant prestige and status can be gained in this line of work, although it can also be lost, depending on how much honor is retained in its pursuit.
2.) Assassination: working as a hired killer. Assassins are poorly regarded by everyone except corp execs. This work is very high risk, very difficult, and often morally repugnant. However, the pay is among the highest of available jobs. Assignments are almost always obtained on the megacorp planets or Aeneas, but missions range throughout the Gemini.
3.) Medical Response (ie trauma team): Medical work carries with it significant status and respect, although the range of the type of medical care provided varies greatly. Some ships are little more than traveling freezers, carrying those in cryogenic stasis to medical facilities on or off world. Others are little more than snake oil salesmen. Most are essentially ambulance equivalents: skilled paramedics, capable of providing basic medical care and some medicines, and of transporting the seriously ill to hospitals. The rare few have skilled doctors on board, surgical suites, or other advanced medical facilities. The risk of this work is low, prestige is high, but pay to labor is typically quite low, particularly for those with a sense of altruism.
4.) Trading: This is the most common of jobs. Because corps rarely bother transporting small cargo on their own fleets, a significant market exists for smaller merchants to make considerable profit in buying and selling. Trading has tremendous potential, but is typically a subsistence type of mission.
5.) Smuggling: like trading, but in goods that are illegal or highly regulated. Risk is much increased from trading, as is the payoff. The very best smugglers are employed by the elite of Aeneas, and get rich as a result.
6.) Corporate Franchise (like trading, except under the aegis of a corp): also like trading, with considerable prestige increase among corps and a considerable prestige decrease among everyone else. Franchises are the favorite target of pirates and brigands. This type of work has about the same risk as trading, with a significantly better payoff, at the price of much of your freedom.
7.) Archeological (Science focus): Precursor study is pursued at a much lower level by the corps than one might expect, and thus this niche is largely filled by enterprising and adventurous scientists. The prestige is low, the payoff is nonexistent, the risk is low. Labor is very high. It is usually difficult to get a crew together for this without 8.) below.
8.) Archeological (Plundering focus): Precursor artifacts, even when little more than slag, are valuable. Risk is low, prestige is low, and the payoff is essentially like playing the lottery. As such, there are far more people in this line of work than is healthy.
9.) Mining/Other resource acquisition: No prestige, high labor, and mediocre payoff unless the resource is very rare or hard to acquire: it's just hard to compete with large scale operations. This type of mission is often combined with archeological, trading, or other types of work.
10.) Racing: Starship racing is, in fact, one of the chief uses for interstellar craft. Not only are such races the favorite type of spectator sport on essentially all worlds, but often significant bets are placed on the outcome. Risk is medium, prestige is good to spectacular, and the payoff is highly variable (very high at the top end, very low at the bottom and low in the middle). Unfortunately, racing is not something easily undertaken without complete devotion: maintaining a ship in race-ready state against anyone other than amateurs is a full time job.
11.) Repair/Construction: Much like medicine, but with a better labor to payoff ratio. This carries significant prestige with it: all the worlds of the gemini are dependent on quite advanced tech, often much more advanced than the tech level of the planet on which it is being employed. Those that can fix or maintain or even sometimes use such technology are constantly in demand.
12.) Political envoy/ambassador/mediation: A position that is typically only attained with significant status to begin with, it si nevertheless a job that brings with it high prestige and high pay. The risk can vary significantly: envoys between the corp planets and Priam are essentially cushy jobs for the sons and daughters of the elite, while ambassadors to frontier governments, to pirates, or to mercenary groups are often in very unpleasant situations, and are more commonly used by high powered people as a svelte way to rid oneself of political enemies.
13.) Spying/corporate espionage: Obviously a line of work with little to no prestige because of the need for secrecy, it is probably the line of work with the highest risk and among the highest pay. While assassins can usually rest easy in the knowledge that at worst they will be gunned down in a failed attempt, spies are deeply despised by even the people who utilize them and can look forward to brutal torture and interrogation in the case of capture, substantiated accusation, etc. Obviously, since no government entity exists on the corp planets to enforce copyrights, security is also a prime concern and thus this line of work is incredibly difficult even for those who are not assigned to Aeneas or other high risk locations.
14.) Theft/Piracy: Another high risk occupation, theft is considered equivalent to murder in many societies in the Twin systems because of how close to "the edge" many live. There is also the fact that most cargo that is worth stealing is protected in some way, so that Theft/Piracy ends up being a variation on #1 much of the time (the two, incidentally, are co-practiced by many groups). Nevertheless, the payoff is quite good and given the size of the two systems and the lack of any real police authority capture is fairly rare (also, most ships are poorly armed, if at all).
15.) Salvage: Another profession with no prestige benefits whatsoever, and with a payoff schedule similar to archeological work. Nevertheless, it is frequently practiced, both because when payoff comes, it is huge, and because it can be easily incorporated into other professions, particularly with sufficiently good sensor arrays.
16.) Police Work/Criminal investigation: As mentioned above, there is no real police except on Priam and the Aenean planets. Everyone else is either a rent-a-cop (read: out of work mercenary or corporate enforcer) or a bounty hunter. Nevertheless, this type of work can be quite prestigious because of the risks involved. Payoff can be considerable, but can also be next to nothing, particularly for those with any sense of altruism.
17.) Computer hacking/programming: Prestige can be large, although only in select circles. Overall, this is a low risk, high difficulty, high payoff type of work: risk can increase significantly depending on what size fish you attempt to fry. Besides the scams and theft variations, programs and virus protection (or hacker protection) are almost as in demand as repair work, with similar benefits and disadvantages.
18.) Prostitution: A steady and profitable form of employment, especially on the megacorp planets and priam (actually, pretty much everywhere). Although only a select few ships support themselves exclusively in this manner, it is not uncommon for a ship to have a full or part time "camp follower" on the crew.
19.) Slavery: Another line of work that is considered by some people to be below them, slavery is actually quite common in a variety of forms throughout the twin systems, notably on Priam and Aeneas. Slaves can be acquired in battle, through piracy, through trading, or through cultivation or tribute: some of these methods are more risky and difficult than others. Slave trading is a profitable business, and for those who pursue #1 and have a degree (perhaps a large degree) of moral flexibility usually not terribly risky.
20.) Surveying: a prestige-less and unprofitable business, it is nevertheless necessary and can turn boring and long journeys into at least a small and steady stream of cash. The need for mapping and measuring the Gemini is constant, since knowing the exact position of every piece of debris in the twin systems is absolutely crucial to navigating them safely (collision with a quarter sized piece of debris at 500,000 km/h is similar to being shot with a railgun). Like salvage, this type of work requires high quality sensor arrays.
21.) Exploration: Like scientific archeology, this type of work is largely unprofitable and provides no prestige. Some pursue this type of work for their own edification, some for the mythically giant payoff that a major find might bring. The amount of money involved in properly outfitting an exploratory ship (cryogenic chambers, huge fuel reserves, high powered ai, advanced sensors, etc, etc) have made this more of a joke than a real line of work.
22.)Passenger transport: next to trading, probably the next most common type of work. Although there are interstellar transport lines, these are usually slow, crowded, and expensive. Booking passage for an extra bunk or two on a ship involved in some sort of other business is usually similar in price and often much more comfortable (assuming the crew isn't morally flexible and sells you into slavery). For ships, it is an excellent way to make some extra money to defray their travel expenses.