I would be considered a novice two boxer but what I do is start a second instance of EQ on the same computer once at the EULA screen on the first instance. The patcher will not run two instances at the same time but you can run (theoretical) infinite instances once the patcher has transitioned to the game. I don't use any third party software. Making in game macros works fine for me. For example, I box a Shadow Knight and Shaman. If it is going to be a rough encounter I use a chain heal macro that looks like:
/cast 1 <------------- Healing spell
/pause 53 <---------- Safely close enough to the refresh for the next cast.
/cast 1
/pause 53
/cast 1
This saves a lot of time having to switch back and fourth.
Two boxing on one system (not really two boxing then I guess) can be done on most machines so long as you don't have spyware and other software running in the back ground. At work when it is slow I sometimes 2 box on a 1ghz P3 with 64 video and 512 SDRAM. My main computer at home is a Core 2 Duo E6600 with 2 gigs and 512MB video. The difference is astounding, I can run full settings on my home computer but have to run the minimum on the work machine with the far clip set to 10%. I have lagged out and died to boss mobs but thats the risk you take on a slower machine. The ideal set up would be two systems, which I have thought about since I have a spare PC at home. This way you can multi task on two keyboards, or gaming pads if that is your thing, and be more efficient with your two character's skills.
As far as the accounts go, if you do not already have two accounts your best bet will be to get EQ titanium at a retail outlet and buy the other expansions seperately. The titanium has the first 10 expansions, which runs through DoD I do believe. You will need to start a new station account and register your keys.
Your signature is for a WoW character so I don't know if you ended up on the wrong forum but... best of luck to you!