What level is your character currently? as i see your biggest mountain at the moment is simply getting gold to start you off. Scrapping your current professions and starting anew will be very expensive if you take two crafting professions or very time consuming if you take a gathering profession to gather the mats yourself.
In your situation i would concentrate on getting to max level(ish) as you get plenty of gold thrown at you as you level, especially in high level content. You will then have a decent amount of starting gold to bump you along in any profession you choose to take.
While leveling you can use your existing professions for a bit of extra gold as you can make bags with tailoring and pets/trinkets with engineering.e.g.
Did you get a scroll of resurrection by any chance? as that will mean you can get an immediate level 80 which you can put an extra set of professions on.
As Hando mentioned the sacred triangle is JC, enchanting and alchemy. If i had to pick two then i would choose JC and enchanting. If you can get a instant level 80 then i would look at putting them on that character so you can boost it up while still using your existing professions for some extra gold. (you may wish to prioritizing that second character then for the sake of getting them maxed out).
Once you have that sorted you may wish to look at dumping tailoring or engineering for alchemy but that will depend on how well your sales are going with those professions.
If you can't get the instant 80 i would level your current character to max level and see about swapping out one of your professions once you have a big chunk of gold to power level another profession.
Last edited by Thefluffyrocker; February 12th, 2013 at 06:05 AM.