(there's something weird going on with the formatting of this post so I've added asterisks as multiple blank lines etc don't work)
** If you want to play around a bit, but nothing too serious (i.e. just to see what VMs are like):
Install in existing windows or linux host
Use VMplayer or VirtualBox
CPU: Dual core with hyper-threading (so you get 4 virtual cores), or quad core (with or without hyper threading). CPU must be able to virtualise - most desktop ones can, but not all. Speed per core is not overly important unless you're setting up something that number crunches alot.
Mobo: Mobo must be able to virtualise. Most modern ones can, but not all.
RAM: 4GB+ (8GB+ highly recommended)
Disc space: Think of 30-40GB per VM you wish to run on top of what the host uses and you'll be fine. This can be juggled as different OS's have different disc footprint sizes.
** If you're a bit more serious (virtualising small to medium computer networks, MS exchange, etc):
Dedicate an entire PC (or server) to the project
Use Hyper-V (bare metal or Server 200R2/2012 w/Hyper-V if you have a spare Server 2008R2/2012 license) or (my favourite)VMware's ESXi (license is free for up to 32GB and one physical processor last I looked)
CPU: Quad core (with (preferred!) or without hyper threading). CPU must be able to virtualise - most desktop ones can, but not all. If you can afford a Xeon or Opteron then get one, but if you're not rich then stick to a dekstop CPU. Speed importance as above.
Mobo: as above
RAM: 8GB+ minimum (16GB+ highly recommended). Server 2008R2 Standard RAM is capped at 32GB and I think ESXi's free licensing caps at 32GB as well.
Disc space: as above
** My home setup (which I use for testing network & server solutions for work and for hosting my mail server+DC) - it's probably a bit OTT :D -
OS: ESXi v5
CPU: Xeon E1650
RAM: 64GB (32GB usuable atm due to licensing)
Mobo: Super Micro Workstation board
Disc: 64GB SSD for ESXi booting, 4x1TB Seagates in RAID 10 for VMs, Seagate 750GB VM backup drive