EVE guys - it's all (most likely) about CPU
I run a few PC's.
Currently I have a 3930k / 3770k / 4770k / AMD fx-8350 all with 32gb of ram and ATI 7850(ish) video cards.
Using lower graphic settings each PC can run 14 + clients smoothly (I judge smooth by being able to run incursions without issues, as having a lot of NPC's on grid seems to tax the CPU quite heavily).
CPU: The 3930k is the fastest (that I have) and can run 16-18 no problem.
Mining? Well you dont need a 6-core intel 3930k for that, I know my older AMD fx-8350 (which is also cheaper by a few hundred) ran 20 miners no problem.
To that point, the 8-core AMD chips are a good bang for your buck in terms of EVE. Yes the intel chips are faster, but if you have $ restrictions, buy the AMD FX-8350.
I've found that asking the CPU to run more then 2 clients per core (the Intel 3930k has 12 virtual cores, 6 logical but that's a different discussion) can run you into performance issues.
RAM: Expect each EVE client to use 1gb of RAM (this is actually around 800mb +) so if your trying to run 20 clients on 16gb of RAM you are not gonna like the results.
Video: Dual video cards would help ONLY if you want to run high graphic settings. Then you could split your clients up among both cards.
SSD's: Frankly I found some good results splitting up my clients among 2 separate SSD drives. Your results may vary, but trying to run your clients from your OS HD (or all clients from 1 HD) will probably hurt performance when warping around. Burst read speed is very important.
Use open hard ware monitor to see how your system is doing resource wise when multi-boxing.
http://openhardwaremonitor.org/
Questions? Find me and a bunch of much smarter people in www.isboxer.com/chat or post here.