I'm looking to purchase a new laptop and I want to know, which brand would be best compatible with #Bitcoin core wallets and upgrades.
Buy anything brand you like, it hardware doesn't matter at all. Every modern laptop/PC will we more than sufficient to run Bitcoin Core.
There are no beter or worse pieces of hardware, just follow the general rule of picking hardware: more expensive = better performance, usually.
What security services should I use?
What do you mean security services? Just download a wallet, protect it with good passwords, preferably use some kind of password manager for that/
And use digital hygiene is a must, install antivirus, anti-malware or even better create a paper wallet or offline wallet to keep the most of your Bitcoins there.