Self custody can be done in stages. I'd suggest researching hot wallets* like Aqua and Blue Wallet, possibly Green. Aqua is great for newbs. Blue has all the bells and whistles and will be able to interact with your future signing device / hardware wallet. 

Learn what your seed / private keys are and how best to store them. Become comfortable moving your Bitcoin into one of the hot wallets.

Then follow the advice here and research collaborative custody with an institution or fully self custody with single or multisig. Either way you'll need a hardware device. 
The good ones:
- @SeedSigner 
- Coldcard
- Jade 

* Hot wallets private keys are generated on the Internet. Cold wallet generates keys away from the Internet and always completely airgapped.

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