There's absolutely nothing to stop you using any processor that you like, but obviously your motherboard must be capable of supporting it. Obviously these days your choice of manufacturer is rather limited. I tend to favour Intel because in my Assembly Language days, they were the processors that I programmed for, but I have used AMD and there's no reason why you shouldn't if you prefer. Your choice of processor will depend mainly on the complexity of your VTPO setup and its possible speed requirements, however I would not recommend using anything less than an Intel PIII running at lGHz or more. That means that old PIII that was going to the dumpster might just be pressed into service as a cheap dedicated VTPO PC, but there again don't expect anything as advanced or sophisticated as Hauptwerk or GigaStudio to run well on it, if at all!
If you're buying a new processor, remember that the OEM versions are much cheaper. With an OEM version you get the same processor as a boxed retail version, but they generally don't come with a cooling fan, pretty packaging and may have a limited warranty, but this shouldn't put you off.
Within the term 'Processor' we'll include the cooling fan as the correct choice could be vital to reducing noise polution in your chosen auditorium. If your PC will be locked away inside a console then it's likely that egress of a small amount of spurious noise from fans etc, won't make much difference. On the other hand, if the PC is actually in any room where the VTPO music will be heard, it's important to have it as quiet as possible and you may wish to consider buying a fan that's known to be quiet. This will also affect your decision to buy an OEM or Retail processor, because there's no point in buying the Retail version, just to discard the manufacturer's fan that comes with it.
Take great care when choosing a cooling fan. Some of the latest models are HUGE and may not fit across the motherboard or even fully inside the case with its covers on!
The general rule with processors is the faster the better within your budget, but not at the expense of perhaps fast memory, or a fast hard drive. If you won't be using a large number of virtual ranks and tremulants, then you may find that an Intel P4 (preferably 2 core) or equivalent will suffice, but with software such as Hauptwerk, that may limit your use to the less memory/speed hungry definitions, possibly resulting in disappointment with the end result. Of course the best results are always the most expensive, but usually worth the extra. The Core 2 Duo (or equivalent) will suffice for a great deal of VTPO work or the ultimate (at the time of writing) an 8 core i7, with the Core 2 Quad (or equivalent) falling somewhere in between. With the latter and sufficient fast memory, I've never had a failure to deliver the goods, even by the most sophisticated resource-hungry software.
Hint: If you're using Microsoft Windows (XP, Vista or Windows 7) and a processor with two or more cores, you can allocate more processor resources to your VTPO software by careful use of Processor Affinity, BUT you are advised NOT to do this if you are using Hauptwerk, as the latest version is optimised to use resources to best advantage and you may well end up finding this a retrograde step. From any program or the desktop, press <CTRL><ALT><DEL> to choose or activate the Task Manager. Once the Task Manager is running, click the Processes tab near the top of the window and look for the entry for your VTPO software (this might be something like "MyFavouriteSoftware.exe") then right-click that entry and choose Set Affinity from the drop-down menu. You can now allocate one or more processor cores for use by that software. This in itself may not gain you much advantage, as you then need to look at all of the other processes that are using your chosen core/s and maybe 'steer them away' from the core/s that you've set your VTPO software to use. by allocating them a different core/s. This is largely experimental and like over-clocking, not for the faint-hearted. Don't be surprised at the inevitable crash and the need to go back a step. This is where it pays to keep a note of each step so that you can re-trace. Obviously you can't adjust Processor Affinity until your system is running so do ensure that any files/definitions that you have written are Backed Up in case you get over-enthusiastic and have to perform a re-install!