You don't need Pro to use
XP compatibility mode, only if you want to run Windows
XP mode - which is a) essentially a free copy of WinXP to run as a virtual machine and b) mostly* useless.
Windows Home Premium will let you set compatibility on a per-program basis, you can get an upgrade version for about £80 or an OEM version (only allows from-scratch install) for about £70, and the full, transferrable version is around £100. Don't get the £50 Anytime Upgrade version, that's for EePCs and the like which ship with the Starter Edition.
You want a 64-bit version, but you can't upgrade a 32-bit version in-place, so will have to run the transfer wizard to copy all your docs to a spare drive, then clean-install and reinstall all your progs. Usually better to do a new OS that way, anyway.
If you're buying a new hard drive anyway, an easy method would be to start from fresh on the new drive, then mount your old disk either internally or in a USB caddy and just copy the stuff over as needed.
32-bit programs run fine under 64-bit Windows - truthfully pretty much everything except the OS and your drivers run in 32-bit mode, 64-bit games are still fairly scarce. Because 32-bit apps run in a protected environment though, a crash in one them rarely spells curtains anymore - you just close it and carry on without lockups or BSODs. The only problem you may have is with
16-bit programs - which some very old games use for their their installers (but not the actual game).
http://www.gog.com/ and
http://www.dosbox.com/ are your answers for those.
Home Premium does lack some advanced networking and policy components, such as workgroups, domains, and remote desktop server, but you're unlikely to need them unless you have a big home network and there are free tools that will do the same job, including virtual machines.
* Windows Ultimate does have the neat trick (which I've never actually managed to pull off) of booting into the guest OS on the virtual drive for those times when only actual WinXP will do, but I've just booted real XP from another disk/partition or used another computer on the rare occasions I've needed that. Virtual machines are usually a non-starter for games.