Jewelcrafting is usually a good place to start because you can essentially supply it with a single type of gathering (mining), and unlike the other crafts that use ore, you don’t have to refine the ore with vendor mats like tin, primordium, or whatnot. Also, the prices of the jeweler-only metals used at the middle tiers (Silver and Gold) are fairly cheap right now.
Cooking is usually not too bad to level, although some mats can be overly pricey (Chili Peppers, for example). Also, many cooking mats can be bought with karma. Just gather whatever you come across out there, and find a good guide for leveling up efficiently.
Leatherworker and Tailor can be relatively inexpensive if you can get leather and cloth scraps on the cheap. Leather in particular is usually fairly inexpensive. Fine crafting materials can get pricey, though, depending on the tier. One way I’ve found to get around buying a lot of (potentially pricey) fine mats when leveling these crafts is to discover/craft bags or packs for part of each tier. This will require buying pricey vendor mats (Runes of Holding), but the good thing about bags and packs is that you can usually sell them for around a break-even price (or maybe even a slim profit) on the TP, and therefore recoup some of your costs.
All of the crafts that involve making weapons are expensive to level right now, mostly due to the high price of the various types of wood. One exception is Artificer, which you can level by discovering and crafting potions. But unlike crafted gear, which can actually be sold for over vendor price now (wasn’t always this way), crafted potions typically don’t sell for much at all, so in that way it’s a money sink.
