If you're like me, you may have some 100 or 110 alts laying around that you just haven't bothered leveling yet because the endgame is disenchanting on them. There's probably a good chance you have at least 2-3 of these cases. I definitely recommend twinking on the server that you have said alts on, because in my opinion if you want to really supply yourself you're going to need three essential toons at highish level.
As someone who farms/crafts literally e v e r y t h i n g on his main server I'd personally recommend one materials toon with double gathering skill (mining/herbalism), one enchanter/tailor, and one skinner/leatherworker. If you have a spare toon laying around with no professions I'd throw in a blacksmith (for heavy sharpening stones)/jewelcrafter (JC strictly for revenue, not for 19s). Having that trifecta of toons, none of which even need to be max level, will secure you on whatever server you are twinking on regardless of its economy or population. It may take you a few weeks of setup and learning the zones / routes for your farming but once you get everything down to a system I am a firm believer that you will find yourself not only with everything you need for your twinks, but you'll be helping your friends out as well / making bank on old world mats, enchants, and crafted items. Since they won't be using their bank for anything else, once you start making multiple twinks with your new resources you can also use their banks to house all your old world mats, or simply use the high level's if they have an empty bank. I use my 19 Alliance druid as the crafting mats bank, and my rogue for all my twink collectible items/BoEs.
Every enchant and crafted item on my Wyrmrest Accord twinks in my signature were made by myself-- and it just saves so much time and money in the long if you weave your farming into other BS you are doing in the game on toons. For example, a lot of the mats I need for all my twinks' enchants I can simply farm while I am transmog hunting. I just disenchant all the gear I don't need, including the non-valuable greens, and I really never have to buy those mats. Once you've got it down, you may be surprised how much can be condensed into multitasking with an hour's work for a week's reward.