A few things to consider as far as new character money goes. (There’s much more involved at higher levels as you start to deal with IOs, feel free to ask once that’s a concern.)
Around 500k will get you through the first 20-ish levels, buying new enhancements as you level up. That’s the standard stuff that you buy from vendors, not the specialty invention enhancements from the auction house. The game is perfectly playable this way, although obviously you can spend more if you want to make your lowbie slightly more powerful.
You can get 500k pretty easy by selling some of the salvage or recipes that you get on the auction house. Almost any rare (orange) salvage sells for about 400k, and you’ll occasionally find a recipe that sells well. Also don’t be afraid to just vendor your common (white) and uncommon (yellow) salvage and recipes. They’re not worth a lot, but they’ll help tide you over until you can sell that first rare, and there’s really no point in keeping them since if you need one you can just buy it off the auction house.
Once you have a character to 50, 500k is chump change. Even basic IO recipes at 50 are a fortune for lowbie characters. Then you can email the cash to yourself by just putting your global name in the To field.
Take advantage of friends! Send me a tell anytime (/t @ineffablebob, hi!) and I can email you starter cash.