If you have a spare computer at home that can be on all the time then you can turn this into a VPN server.
If you have a router with DD-WRT (it may even have built-in VPN server capability - but not many SoHo ones do) or other custom firmwares then these can also be used as VPN servers that use OpenVPN.
A little research and trial and error on your behalf would have found many hundreds of results and guides on how to create a home VPN.
I would strongly discourage you from trying to create your own encryption mechanism - it's just not worth it and will inevitably be extremely insecure.
Use, for example, OpenVPN - it's tried and tested.
The only thing you will need to consider is whether you have a static or dyanmic public IP for your home Internet as you'll need to check a dynamic IP quite regularly to see if your modem has renewed this as it may be different and if you're away and the IP changes you'll not know what it might be so might not be able to connect in. Dynamic DNS services can help with this or you may have/be able to get a static IP from your ISP so you know it won't change.