Gus,
as someone else said, best chose an already approved design. The GP4 certainly isnt approved. The Glasair III isnt PFA approved as its outside the PFA remit- too powerful engine. But a couple have been built on a CAA permit. Probably much more expensive to get done under the CAA.
The Glasair II is a PFA approved design though, quite a few flying in the UK.
Other fast aircraft are any of the Vans RV range- over 100 of these flying in the UK now, or Lancair. slightly slower, the MCR01 or Europa.
Getting engines is easy, many kit manufacturers have deals going with the engine manufacturers- Vans aircraft are the biggest customer worldwide for Lycoming O-360 engines and do a good deal for Vans builders. New Glasair presumably have a similar deal. Props similarly can be sourced thru the kit suppliers. Otherwise there are plenty of companies in the UK, US and elsewhere who will sell you engines, props and anything else you need. Some also sell overhauled or just "used" stuff
For the UK the best place to look is in the PFA magazine, some info also in the adverts in the other flying magazines, Pilot etc.
Also get yourself a copy of "Trade a Plane" which is a US paper which is full of aircraft/engines for sale and adverts from all of the major companies involved.
Come along to the PFA Rally (or Flying For Fun as its now called) July 1-3 at Kemble. This is the largest GA event in Europe and you will see examples of most homebuilt aircraft available in the UK flying in and exhibitors selling most of the kits and equipment that is available
good luck!