Exchanges like Coinbase are convenient for buying, but they're not the best place to stay long-term, especially if you have significant amounts. The difference between hot and cold wallets is simple: a hot wallet is connected to the internet (app on your phone, website, exchange), while a cold wallet is offline. Cold wallets are much more secure because your money can't be hacked remotely, but they're slightly less convenient if you want to trade frequently.
For someone just starting out like you, the best choice is probably a hardware wallet like Ledger or Trezor. It costs around thirty euros, it's physical like a small USB stick, and here's how it works: it keeps your cryptocurrencies offline but still lets you send and receive them whenever you want. The process is easy: you buy the device, initialize it, and from there you manage transactions through the app on your computer. Your bitcoin and ethereum stay safe inside the device, and even if someone manages to hack your PC, they can't touch anything because the private key stays in the physical wallet.
If a hardware wallet seems like too much right now, as a temporary solution you can use a decent hot wallet (like MetaMask for ethereum, or a reliable mobile wallet like BlueWallet for bitcoin). It's not ideal for the long term, but it's infinitely safer than leaving everything on Coinbase. And when you're more confident and maybe have accumulated more crypto, get a cold wallet and move the part you don't touch over there.