An autograph from the Lovesexy period is almost certainly your best bet as Prince promoted both the record and tour with some in-store signings. I think he did 2 or 3 in London, at least one in Stockholm and some in the USA. That said, Prince autographs are very, very rare (well authentic ones are).
You will struggle to find anything genuine from the Diamonds and Pearls era as Prince had largely stopped signing other than a few in-store signings of his symbol. He also signed as "Tora, Tora" briefly in the mid 1990s.
It is highly unlikely you'll find anything signed Prince or even initialed as "P" after the late 1980s.
You're welcome. If you see anything then post here for an opinion. Just after Prince died, eBay had a lot of fake Prince signatures. I think it has calmed down a bit but as with any rare autograph, there are charlatans out there. So it's wise to check first.
Plus read through the posts here and you'll start to get any eye for spotting Prince's (often very elegant) hand writing.