Best budget telephoto lens Sony E mount ?

Hey everyone! I’m looking for a telephoto lens for my Sony a6500, and I’d appreciate some advice. I’d like to use it for street photography, nature, and maybe a few event shots. My budget is:

Up to 600€ for a second-hand lens

Max 700€ for a brand new one

Could you recommend any good options that are compatible with the Sony E-mount? Thanks a lot!