You can access your laptop remotely if you set up Tailscale and register your laptop with them. It's a VPN, so it's like having your laptop and other registered devices connected to a local Wi-Fi all the time.
It's not too hard to use your own domain and it is certainly worth it. It can even be cheaper price-wise if you go for providers that specialises in "bring-your-own-domain" mail providers. Used to use MXRoute, but I switched to NameCrane because their deal was even cheaper. It's still available, I think.
The only disadvantage I can think of is that you need to take care of your domain. If you let a spammer spam with your domain, you might ruin your domain reputation, in which case your domain might get blacklisted. Also, try to stick to well-known TLDs (.com, .net, etc). Domains ending in .xyz is usually filtered out because it's commonly used by spammers.
I use "proper" a lot, so that one is inevitably favourite, unless it's not an exclusive UK slang