Several practical solutions here but the simplest is probably to start with thunderbird on your home computer. That way storage limit shouldn't be a worry and you can see if you find it searchable/usable enough. If so, you can do a Google takeout as a long term canonical archive, do a thunderbird backup to easily switch computers when the time comes, and then sign up for a privacy friendly service.

I bought into proton for a bit but am very very against how they bundled their services and switched my mail to posteo, which i have had no issues with in the last 1.5 years or so. Tutanota was fine but firmly a third place opt for me. I also prefer posteo because I'm anti-magic: posteo has tons of options which can get you to same or better security than proton, but it doesn't "just work" like protons security does. Both are great.