vCenter Server

You can use anything that runs Windows 2003/2008 decently.

You can just create a vm for vCenter Server, just ensure the DB is backup regularly
This is normal setup even for enterprise environment
You dont really need a super fast machine for VC server

i just found this (page 16 min requirements)
http://www.vmware.com/pdf/vsphere4/r40/vsp_40_esx_get_start.pdf 

2CPU, 3GB of RAM etc

yes it is, what are you implying? your esx host cannot allocate the required resources?
then you should get a dedicated host instead

If you're looking at HP I would go with a DL360 G5/G6 with 6GB RAM and Windows x64 OS.  If you don't have a dedicated SQL Server you can use SQL 2005 Express instance.  3 72GB SFF drives should suffice. A dual core should suffice you could always another in the future if needed, with your configruation I would doubt it.

A more affordable option is a DL320 G5, it uses unbuffered memroy and is somewhat more affordable.  It usually comes with 2 160GB SATA drives and you can put in up to 8GB RAM.

The nice thing about using a x64 OS is that you can then have the capability to integrate other apps if needed  on the same box such as vmware backup software, etc.. items that need to integrate with vCenter.

The VC server does not to be a high end server, if you're using SQL on it (do not use the express edition, it has a limit of 4 GB database, it could space out. For a small environment it can be used -costs-) you need a bigger machine to run sql.
If you want to run more applications on it (reporting against your database, or more reporting tools), you should also have a bigger machine.
My advice would be to take a virtual with VC on it. Start with 1vcpu and 2-3 GB mem, you can always scale up.

Does Vcenter have to be installed on Win2003 /08 ?

You can use a 32bit windows 2003 or 2008 host. If you are managing a lot of hosts (200) vmware recommends a 64 bit os
http://www.vmware.com/pdf/vsphere4/r40/vsp_40_esx_vc_installation_guide.pdf