IMHO, I'd avoid the chemical stripper. Too many opportunities for some to soak into a crevice and not get rinsed out and neutralized properly. Then after you have invested all the work in primer/paint (even if you give it a budget paint job), it would be a shame as you sit back and enjoy the fruits of your labor to see the paint bubbling up in a crack due to some chemical stripper left behind.

Start out w/ 80 grit and see how deep the primer goes. It may surprise you how much paint is actually on there. I used chemical stripper on a truck once. Even after what I thought was an adequate wash down to neutralize, the paint let go about 3 months later. Only thing I could ever deduce was that it was the stripper in the crevices. This was on a 1963 GMC Truck.