ESXI is definitely what you need, running that many vm instances will require a few cluster of servers for load balancing and performance purposes.
I would suggest you to buy a couple of Dell servers, they are a bit cheap compared to other vendors and they can also be customized to your needs.
Check out the Dell's T610 servers, http://www.dell.com/au/business/p/poweredge-t610/pd they are ideal candidates for small to medium server virtualization projects.
Since you are running that many VMs, you should maximize the ram capacity in those servers, as well as look into ways for maximizing your server I/O performance, or things will get sluggish.
SSDs are very good candidates for maximizing throughput, you might want to look into NAS devices, that supports them. Ensure your servers are using 10Gigabit Ethernet adapters, instead of 1Gigabit or else they will get saturated very quickly, if the servers are under heavy load.
And that could affect the performance of other VMs as well
Edit: You will find these links quite informative.
http://www.vmworld.com/thread/3184
http://www.itworld.com/answers/topic/virtualization/question/how-many-virtual-machines-can-i-run-one-system