Prince's main guitar amplifier from the late 1970s to the early 1990s was his Mesa/Boogie Mark II. He used it live and in the studio and appears on many of his most popular recordings, including Purple Rain.
Prince first used the Mark II live on the Prince tour, but it is possible that he used it in the studio before this time. He initially paired it with a Marshall 1960a 4x12" cabinet, but later moved to Bag End D-12M 2x12" cabinets. Prince did not always have an amplifier or speaker cabinet on stage, but it is likely that he used this on every tour up until the Diamonds and Pearls tour. Prince also used his live set up in the studio. There are reports of Prince using this rig on the Purple Rain album, and it is likely that the Mark II/Bag End set up appears on most of his recordings from the 1980s.
The first Mark IIs that Prince acquired were IIB models. He had two by the 1999 tour and acquired an additional IIC+ model for the Purple Rain tour. The IIBs were upgrade to IIC+ specifications. One of these recently showed up in a Minneapolis music store.
There are claims that Prince ran his Mark IIs clean and used his Boss pedals for distortion. However, he usually had a channel switcher onstage and later ran separate clean and dirty amplifiers. He also used the low-gain Boss SD-1 Super Overdrive. This would not produce the kind of high-gain distortion Prince was known for but was commonly used to boost an overdriven amplifier. This was typical for 1980s hard rock and metal music. It is most likely that he ran a distorted Mark II, with the SD-1 used for an additional gain boost.
Prince switched from Mesa/Boogie Mark II to Mark III amplifiers at some point in the mid to late 1980s.
I’m recalling that Prince didn’t use the Lead mode anyway, but his setup back then was definitely a 300 series [Mark II] head with two Bag End sealed-back cabinets loaded with JBLs. It was quite a sound!
For my guitar, it was a Boss compressor, probably a CS-1, directly into a TC Electronic distortion pedal, into an MXR boost, into a Cry Baby Wah, then my chorus, the brand of which escapes me right now, and then into a volume pedal, all of which fed into a Mesa/Boogie Mark II head on a cab with, I think, a pair of JBL speakers. I was using one of my modified purple Rickenbackers when we recorded it.