My advice - do not fall into the trap that you can run e-mail better than a provider who does that for a living.
The easiest way imo is to pick a provider who specializes in this sort of thing. Then begin to rotate your accounts from the old account to the new one, utilizing aliases or masks as needed and desired.
as you do so , archive old emails off your old account. Periodically check but remove it from your daily driver. At some point, all will be left is spam at which point you can … let that mail provider manage for you.
Many mail providers have excellent spam protection so you are right - get it at the source.
Depends how much your time is worth? For some it is easily worth the $1-$5/USD Month to let your mail provider handle the bulk of it.