Here's a few websites you can also look at that have free downloadable plans... thousands of them. It's just something for you to research... as you'd mentioned research and building, but not really whether you were looking for a kit or plans... between these 2 sites there's probably over 10,000 planes of different varieties to look at and/or download plans for. Many are advanced builds, many are well within the skills of alot of people.. and fall in the trainer category too... it depends on where you're at in the skills and resources.. and plans building isn't for everyone... but it's something to study.... and if you find a plan you like, just take it to a local print shop if there's one available and have them output a set of plans... or you might even be able to print them at home in a tile format too... or just download to your computer and study ...
www.outerzone.co.uk
www.aerofred.com
As the others have mentioned there's many good builders kits on the market also... Sig has some great builders kits in the trainer category, as does Great Planes and a few others. There's also some laser kit cutters that have nice kits available...
I'm just suggesting these sites as a glimpse into plans and ideas... the easiest, and probably the best way to get into building is probably a good builders kit though.