The best wallet is non-custodial wallets: Bitcoin Core, Electrum wallet. If you don't want to spend too many storage space for your wallet, Electrum wallet is the best, it is a SPV wallet and does not require too much storage space.

[GUIDE] How to Safely Download and Verify Electrum. Verify your Electrum wallet as the guide topic shows.

Gambling sites have strict rules for deposits and mixers/tumblers. You have to read their rules about Tumbling, mixing in either FAQ or ToS (Term of Service). Try to search with KYC, AML, tumbling, mixing, etc.