I have never had much trouble with temperament changing too much with proper nutrition, as someone else has said… they usually get better!
But, I did have one horse fairly recently that was just awful when he started being well taken care of. Kind of makes sense why he came in the condition he came in. This was also a horse that my gut feeling was no, but I was bored and bought him anyway.
Your budget is good enough that I would look for a young WB.