I'm not sure what kind of money you want to spend. I will say, I have the 70-300L (currently on loan to our youngest son) and it's amazing. Fast focus, not that heavy (weight is relative: my wife prefers her 55-250 STM because of the weight advantage), easy to pack in a camera bag, etc.
I used it for quite a while and got some amazing photos with it. I'd still be using it but I was able to save enough to buy a 100-400L ii.
I've seen two or three 70-300L's show up on POTN for sale in pristine condition. I don't know the final price but the ones to which I am referring were listed at $700. I paid $1400 for mine and got every penny's worth. At $700, it's a steal.
Edit: I was typing my post after yours posted, bmax. I know $700 is a lot... way more than the 55-250 STM. As I said above, my wife could have inherited my 70-300L but stayed with her 55-250STM. She loves it. I edit all her stuff and personally, I can tell the difference between the images each lens produces. That said, she's an excellent photographer and her stuff with the 55-250 STM comes out nice.
Kim (the male variety) Canon 1DX2 | 1D IV | 16-35 f/4 IS | 24-105 f/4 IS | 100L IS macro | 70-200mm f/2.8L IS II | 100-400Lii | 50 f/1.8 STM | Canon 1.4X III
RRS tripod and monopod | 580EXII | Cinch 1 & Loop 3 Special Edition | Editing Encouraged