In general, Force Users will want to look at Artifice and Synthweaving, Non-Force Users will want to look at Armormech and Armstech. Cybertech and Biochem are of interest to all classes.
For Gathering and Mission skills, simply choose the ones that best compliment your choice of crafting skill, or, if so inclined those you feel will be most profitable.
Some things to note about the specific value of each skill:
Biochem is likely the most useful at endgame, as it's the only skill that is capable of providing an item that fills a recurring player need (Stims/Medpacks), and which is not purely replaceable with drops. Of particular note are the reusable Stims and Medpacks which Biochemists can make for themselves. As far as equipment goes, Biochem also provides recipes for Implants, so you can reliably fill and upgrade two equipment slots for yourself and any companions as you level. Biochem is a great choice for players that prefer to rely heavily on consumables, and don't mind relying on drops and vendors for gear.
Cybertech is the best choice if you are intent on using orange items to maintain a specific 'look' for your character and or your companions. Cybertech provides the Armoring and Mod slots for these items - two of the 4 slots found on most Weapons and Armor. In addition, Cybertechs can fully outfit Droid companions, as well as producing Earpieces for themselves and companions (filling one equipment slot with up to date gear at all times), and Ship Upgrades. Finally, Cybertechnicians get to make their own cool custom speeder bikes. Cybertech is a great choice for players who prefer 'custom' (Orange) armor, classes that rely on droid companions (Trooper, Jedi Knight, and Imperial Agent, or anyone who is fond of the Ship Droid), and those who are very fond of space combat missions.
Artifice is primarily aimed at Force Users, but others can make use of this tradeskills ability to create Color Crystals and Enhancements. The former are used in Blasters as well as Light Sabers, and most orange equipment has slots for the latter. While a Lightsaber user will benefit more, it's not a horrific choice for others. One notable limitation is that very few companions use Lightsabers, so Artifice isn't the best choice for outfitting them.
Synthweaving is almost exclusively useful to Force Users. It provides no notable crafting recipes of interest to folks who prefer Blasters to Lightsabers - and since non-force users don't have any 'Jedi' companions availiable to them, it's not even useful for equipping companions. However, for Sith or Jedi characters, Synthweaving is a powerful choice, as it will ensure that you always have up to date gear availaible for yourself, and at least some of your companions.
Armstech fills a similar role to Artifice for Blaster types. Unlike Artifice however, it provides little that would be of interest to a Force User beyond companion gear. Also unlike Artifice however, it is much more useful for equipping companions, since most of them do use Blasters, Vibroswords/knives, Scatterguns, and other weapons of the sort that Armstechnicians can craft.
Armormech is similar to Synthweaving for the pew pew set, but again, like Armstech, is much more useful in equipping companions. Like Armstech, it provides little to nothing of interest to a force user, who should skip it for Synth.