Here's a list.
The trick is that you need to try to find what works for you - I've had good luck with CPVC around me as a very inexpensive barrel material, but I hear reports (from Captain Slug, among others) that they can't find any that is worthwhile. Brass sounds nice, but is expensive. PETG only works if you get the right PETG. I find it's best to either get materials you can lay your hands on and test your darts in, or get materials specifically indicated by very reputable people.
Brass may need to be nested (i.e.: sheathed into something else to increase the outer diameter of the material) into something else to get it to fit in the stock grey old-mega TTG barrel. If you modify the shell to take it it'll work just fine, but you're on your own for fitting then.
IIRC Thick-wall PETG is better for springers than other types of PETG.
Your confusion about barrel fit is due to a looser fit being traditionally prefered for pneumatics. They used to be more high-volume low-pressure deals, and worked well with longer looser barrels (Like a HAMP). Springers, on the other hand, need a tight fit to keep pressure building behind the dart so they can generate maximum power - they don't have nearly the volume most pneumatics do and a loose barrel would just rob power. More modern research suggests that tighter barrels on more controlled pneumatics are also desirable, so the loose fit of old may just go away except for HAMPs and blowguns. Anyway, your ideal barrel fit for the TTG should probably be an extremely tight ring somewhere in the back 3rd of the dart, a moderately tight fit along the rest of the dart, and an even fit at the front. Failing that, I find CPVC that is difficult to put a dart into but not so difficult that it bends when inserted works great - I can hit 100+' (likely angled) with these things so I'm not miffed about finding the perfect fit.