@OP I think you're meant an exchange, not a wallet isn't? as you said you want to make money on crypto and don't want to lose a lot money.
The most safest wallet is hardware wallet which cost minimum of $50. Hardware wallet is non custodial, you can't buy coins from there, you need an exchange to buy crypto.
I don't think P2P or DEX is convenient for trading, so I recommend to use CEX. When you have buy crypto in CEX, you need to pay trading fee and when you move your coins to your wallet, you need to spend more money for withdrawal fee. I heard Kraken seems offer a cheap trading and withdrawal fee, but I don't know now since the fee is quite higher than before.
BUY CRYPTO IN LEDGER LIVE
https://www.ledger.com/blog/buy-crypto-in-ledger-liveThis feature, operated by our partners Coinify and Wyre, is available directly in the Ledger Live application. Pick your favorite crypto among Bitcoin, Ethereum, Bitcoin Cash, Stellar, USDT, Polkadot, Litecoin, Chainlink, MakerDao, Dogecoin, Uniswap, Compound and many more. Find out more about options, eligibility and payments methods here.
https://www.ledger.com/blog/buy-crypto-through-ledger-which-provider-is-made-for-meBut if you want to be anonymous, it is better to buy cryptocurrency for cash.