Not quite, you're mixing up the Bitcoin software for running a node with a wallet - they're different things. Your steps are:
1. Sign up for an exchange.
2. Deposit cash (with card, bank account, whatever else the exchange supports).
3. Buy Bitcoin (or some other cryptocurrency).
4. Transfer the Bitcoin to whatever wallet you want (or don't transfer it, totally up to you).
Your link to https://bitcoin.org/en/download is for the software for running a full Bitcoin node - this isn't what you're looking for. Running a node is different from using Bitcoin and it's different from buying Bitcoin online. What you need to use instead is a wallet. Have a look at the getting-started resources on the official site (or on Coinbase if that's the exchange you're using).
The fact that you're on a Mac doesn't matter - wallets are widely available for any mobile or desktop OS. The fact that you're in the UK only matters as far as choosing an exchange that operates in the UK (but most of them are anyway).