So any of the batteries I mentioned will work in the AE-1P correct? As long as they are 6v?
I would avoid the lithium batteries, but only because they are different from the alkaline and silver-oxide versions, and didn't even exist when the AE-1P was current.
This is at least partially influenced by the fact that Mamiya used to advise against the lithium versions for some of their 645 cameras that took a PX-28 battery - apparently the differences mattered to those cameras.
“Photography is a complex and fluid medium, and its many factors are not applied in simple sequence. Rather, the process may be likened to the art of the juggler in keeping many balls in the air at one time!”
Ansel Adams, from the introduction to The Negative - The New Ansel Adams Photography Series / Book 2