Software for a VPN connection to home from work

Since you don't want to use Team Viewer then there are a couple of options. One is to use a router that supports a third-party firmware like ASUS Merlin or DD-WRT. I use an ASUS router myself with ASUS Merlin and have a local VPN. I can connect to my local FTP and Team Speak server without opening ports. Best of all, it looks like the VPN port that is used uses port knocking. I have scanned my network with Nmap and check my external IP at Shodan, Censys and GRC's Shields Up and no port is opened. Yet I can make a VPN connection.

Now if you use a router then you'll have to go into your ISP's modem and turn on bridging mode in order for the router to work with the modem.

If you use a VPN in a router you can install on the home computer something like Ultra VNC or Tight VNC. Then what you do at work is launch the OPenVPN client, make a connection top your home router and then fire up the VNC connection.

The other option is LogMeIn by Hamachii. Absent of those two solutions and TV, you're stuck with RDP.

Note that you can find routers already flashed with ASUS Merlin or DD-WRT on eBay. If you go that route, I'd make sure to flash it again or update its firmware. And make sure you stay abreast of updates. Updating is a simple as browsing to the router update file via the router.

If yo want to go cloud/NAS, there is the option of Amazon AWS S3 and using the FTP client WinSCP to connect to your AWS S3 bucket.

The first year has a free tier providing you don't go over the limits. After that it's pennies a month. I offload attachments on my own website to S3 and it costs me about 63 cents a month.