I'm just gonna second everything elisi said. Seven is just much more modernly paced to begin with, and many of his stories are only three episodes long. It's definitely still an adjustment, so you have to be a bit patient, but once you've gotten through those seasons you're far more acclimated to the pacing and other allowances you need to make to watch old tv and it's easier to go farther back. Also Seven's episodes have a lot more of the meaty character stuff that you expect from the new show (mostly for the companion, rather than the Doctor, but it's good stuff), and a solid percentage of the stories have just really stellar trippy, poetic, ideas-packed things going on.

Picking and choosing random stories is the worst way to get into Classic Who, and I wish somebody'd told me to just pick and era and watch it in order years ago.

And Five is the best thing since Twelve, basically. It's less in-your-face, but if you want modern Who kinds of self-reflective psychological complexity in your Doctor, you want Five. I kinda went into Classic Who figuring that I'd very much enjoy watching the Classic Doctors, but not that they'd actually be, you know, ~interesting. But oh. I was wrong.