There are lots of ways of doing this -
Possibly the easiest is to use software like Teamviewer, which allows you to run teamviewer in an "always-available" mode with a username and password. The disadvantage of this is that your server will always run through the Teamviewer servers, and depending on your usage case there may be a significnt license cost (but it might be free). The advantages are no port forwarding, VPN or IP addressing issues.
The alternative way is to use some kind of remote deskop (like built in windows RDP). This will require a method to connect inwards to your PC. This can be achieved using
A professional way to do this would be to set up a VPN into your system and then connect across that to do RDP. There are a few ways to do this - none of them trivial. They would most likely be variants of this:
Use a static IP address (or dynamic DNS service) for your router and run a VPN server on your router. You need to ensure the VPN service advises the VPN server of appropriate local routes for your home network, and then run a VPN client from your remote laptop to the server - in this way you secure the connecion. Unfortunately "VPN server on your router" requires a decent router and/or after-market firmware like DD-WRT. Its also not trivial to set up (but plenty of online guides).
If you don't want to use Dynamic DNS and don't have a static, you could also set up a VPN server on the Internet (eg using AWS or a Low end VPN) and run VPN clients from both your server and laptop to it. Unfortunately this probably requires a fair bit of knowledge- most likely Linux command line knowledge - and there will be a cost for the virtual server as well.
Did you already consider Windows Remote Desktop Connection? If so, why is it not a valid solution? – Tetsujin – 2018-08-25T09:51:23.680
What operation system running on that old laptop? – Alex – 2018-08-25T12:29:24.747