They technically already have two things that would be perfect for you!
There is Windows XP Starter which was pre-loaded on Netbooks but also sold standalone in third would countries. Its very limited but DOES run pretty much any app you throw at it. Its very slimmed down and runs on very low end hardware.
Then there is Windows Fundamentals for Legacy PC's which strips out the bloatware already and is just core Windows XP with the unneeded apps, resources, etc installed. If you want to have it as slimmed down as possible, I highly recommend this version. It was developed for older (Win 98 era) PC's in mind and runs amazingly well. If you want the apps they removed back, you can install them yourself.