Most door dealers can get large radius track...any door dealer can get high-lift. If you have a door dealer that carries CHI brand doors; CHI has 10", 12", 15", 20", and 32" radius tracks. Most manufacturers have 12", 15", and 32" now days. Maybe others can offer manufacturers with other options too.
In general, the larger the radius of track, the smoother the door rolls up/down. Many door dealers that have "stock" doors will stock 12" radius and install it of whatever job they sell (every if a greater radius would have fit). In my opinion, 15" radius rolls much smoother than 12", but 12" fits in alot more residential applications. 10" is pretty tight for me.
With high-lift track, you go up the wall, but still can choose a radius for the horizontals. Most places go up the wall as needed and then use standard 12" or 15" radius horizontals.
Given the choice of high-lift versus a large radius track such as 20" or 32"...assuming I get the door to the ceiling with both applications, I'd probably go with the large radius track...again...because I think the door rolls smoother. And because I have more opener options. Now, this is my personal preference and logic. Maybe others would rather do the high-lift and will post why.
Currently, I'm working on my own garage and will be putting in a new garage door. From the top of my garage opening to the ceiling, I have 22". By the book, 32" radius track will take me up to 24", which is slightly too high. 20" radius will still be a little low for my liking. Nice this about high-lift setup is that I can get EXACTLY what I need and put that door just where I want it. Now, can the 32" radius be made to fit...maybe??? I might just give it a try to see.