One of the cheapest, and easiest crafts to start out on, for people with low cash is Clothcrafting.
Just go to Windurst, and run around Sarutabaruta, or Tahrongi Canyon with a low-level job, about level 10-18 so you can get crystals, and take out lots of Yagudos, Mandragoras, and Bees and Crawlers (make sure you've got your signet on).
{{If you have a job that can take out Elementals, just kill those, for crystals, instead.}}
All the basics needed are Yagudo Necklaces, Wind Crystals, and Earth Crystals. Yagudos are your primary targets, since they drop the Necklaces, which can be turned into Grass Thread with the Wind Crystals, that they also drop.
1 Wind Crystal + 1 Yagudo Necklace = 3 Grass Thread.
Other useful mobs:
BEES: Wind Crystals, Beehive Chips (those also sell well)
MANDRAGORA: Unless you're hunting the ones in Tahrongi Canyon,
These are just for Earth Crystals, but their other
drops (4-leaf Mandragora Bud, Yuhtunga Sulfer,
Cornette) can be traded to Yoran-Oran for gil and
Windurst fame. You can steal Saruta Cotton from
them, which is useful later.
CRAWLER: I don't think I need to tell you that Silk Threads
sell well in the AH. Also drops Earth Crystals, and
Crawler Calculus (another source of fame/gil).
Keep cranking out Grass Threads, and use them to make Cloth.
Earth Crystal + 3 Grass Thread = Grass Cloth.
This will cap your skill at 4, and you can either sell all the raw materials or use them to push your skill up a little higher first. Usually Grass Cloth sells for around 4K on the AH. It's a nice steady source, since these raw materials sell at a regular pace.
You can continue making Grass items up to around 9 or 10 skill, and then move on, to Cotton. Saruta Cotton is not overly difficult to get, with all the mandragoras running around in Tahrongi Canyon. You can Steal cotton too, but you will need to gain a steady source of Lightning Crystals to help you in this phase. It may be a little slow or difficult, at times, but it will pay off in the long run, as Cotton Cloths are a very HOT item in the crafting section, especially since the coming of Noct and Sage gear. You should be able to pull in 10-13K per stack of this stuff.
Lightning Crystal + 2 Saruta Cotton = Cotton Thread
Earth Crystal + 3 Cotton Thread = Cotton Cloth
The only thing, in the Sarutabaruta/Tahrongi Canyon Area that drops Lightning Crystals, that I know of, is the armored Goblins (Fishers, Butchers, Tinkerers). Slight investment may be necessary to gain these, instead.
So, anyway, that's the basics. Very little investment is needed to get this craft moving. It mostly takes time. It starts to pay you off, in small, but steady increments almost immediately. I still use this craft, as my main income source, to propel my other ones.
Good luck.