The budget you have set forth is actually quite generous!
Some basic questions to get us started?
Do you shoot on location much? Or just in studio?
I ask because at some point, you will have to choose either a system with a power pack(very common, high powered), or mono-lights(common with budget minded photographers, low power).
In general, a MORE simple setup reigns supreme. SO, I would recommend against more lights over fewer lights. Three lights feels extraneous to me, as I have two flash heads, and rarely use BOTH.
You may(or may not) want to consider a large, high quality modifier as part of your new setup. Chimera is a colorado based light modifier manufacturer who makes extremely high quality products at reasonable prices.
Additionally, a beauty dish seems to always be a useful tool to have in your arsenal, although I have never seen one in use - I just use a medium 3x4 foot soft box(from chimera)
(some of you may have seen this coming)
Speedotron black line lights, which are cheap and relatively easy to find on craigslist or ebay, will give you an awful lot of bang for the buck if you find a decent set USED. I found my 2400 watt second power pack, and two flash heads, and two chimera soft boxes for $750. That, to me, was a worthwhile investment.
Other options include the Paul C Buff Einstein640 monolights, however they offer a max output of only 640 watt seconds - which can be enough for most applications. Paul C Buffs modifiers may leave something to be desired, but they have a great return policy, and a large variety of useful toys and tools to choose from!
-simple light setup
Look at that, I didn't even once bring up tethered shooting.