"Bitcoin Wallet" wallet on Blockchain.com is a "non-custodial" wallet -- this is probably what you want, and it'll let you send and receive Bitcoin to and from a wallet with a key that you own. You can import this key into other wallet software if you ever need to.
"Bitcoin Trading" wallet on Blockchain.com is a "custodial" wallet -- meaning it's a balance held on Blockchain.com, similar to a balance you might hold on any other exchange. If you want to buy or sell Bitcoin using Blockchain.com then you'll need to sign up for this, and it'll require you to upload identity verification documents.
To start mining Bitcoin you will need to purchase an ASIC. To mine Ethereum you'll need at least a recent high-end GPU, software such as Ethminer (https://github.com/ethereum-mining/ethminer/releases), and to join a mining pool.