I chose the first option, because it's about as close as I could come to my reality...I've changed out belts for different reasons...I started with my original belt, then I bought a new one when I was promoted to 2nd Dan. On that one, I kept adding new stripes until my most recent promotion to 4th dan. That particular belt I keep hanging on my wall because, really, it has too much embroidery for my tastes these days. As for my original belt, I had nidan stripes put on one end, but was promoted in TKD so I started wearing that association's belt that I was presented with. When I went home, I would wear my original belt.
When I was teaching in Iraq, I purchased a simple Tokaido black belt, no embroidery, no stripes, nothing but belt. That's the one I wear when I'm not wearing my kenpo colored belt(green right now)... once I eventually earn my black belt in Kenpo, I'll probably go back to wearing that Tokaido belt in kenpo as well.
By the way...I trimmed the stripes off of my original belt, hemmed it up professionally and put it into storage in hopes of presenting it to my son in about 15 years (or in fairness, my daughter in about 18 years).