For you, the path is this:
Spousal Visa: Valid for 33 months from date of issue. You already have this, of course, and you probably have an expiry date on your BRP of somewhere around December 2020 or January 2021 (?). Sometime between from 28 days before you have been in the UK for 30 months (28 days before 4 September, 2020) and the expiration of your BRP, you will need to apply for Further Leave to Remain (FLR(M)).
FLR(M) (Further Leave to Remain): Valid for 30 months. This is the next step. It is an extension of your limited leave to remain in the UK to get you to 60+ months to qualify for Indefinite Leave to Remain (ILR).
ILR (Indefinite Leave to Remain): After you have lived in the UK for 60+ months, you are eligible for Indefinite Leave to Remain. This is the final visa, and gives you the right to live here indefinitely, as long as you don't leave for more than 2 years. You can work on this visa, can access public funds, and pretty much do anything a citizen can, except vote in elections.
As the spouse of a British person, you can apply for citizenship as soon as you have ILR. You don't have to apply for citizenship, but you will be eligible for it. If you do get citizenship and then move out of the UK, you can stay in the other countr(ies) for as long as you want and still be a British citizen and can come back at any time.