If you don't care much about crafting, I don't think anything is lost by just getting Slicing and just doing that until 50. You'll have lots of cash, and I can see Ghoselle's point that at 50, crafting becomes stupid fast with 5 companions ready to do your bidding.
For a first character, biochem-bioanalysis-slicing is a decent choice.
I have yet to dive into bioanalysis/biochem, but this strikes me as very sound advice.
An alternative for first characters if you know you're going to be an altoholic: slicing, treasure hunting, something. Treasure Hunting generates lockboxes as well, but they tend to have green items rather than cash. (And even when they have cash, I think they're still a net loss, unlike slicing, which tends to be a net gain.)
So then you're generating tons of greens for the eventual members of your family. I think if you just automatically vendor the greens, then TH isn't so much of a credit sink as it could be.
Another option is slicing plus two gathering professions (expect to be distracted by gathering a *lot* if you do this), although you may not have a lot to do with the gathered mats since people don't need to buy mats off the AH much. You can switch to a crafting profession at level cap and use your gathered mats to level it very quickly.
It's worth remembering that WoW doesn't have reverse engineering: you get mats back from shredding your own stuff. At least for level 1 materials, I only needed about 50 of the two types to be done getting skillups. This gets harder at higher levels of crafting, as there are more than two material types.
So my point is: I suspect if all you did was gather, you might have a million billion thingies, and once you got around to crafting, you might have 90% of them left. It's not like levelling WoW blacksmithing where you need 23948723947824 tin to get to iron.