If all you're doing is transferring files, set up a secure ftp server (sftp; I believe putty has a server/client pair). Or set up an ftp server (most are reasonably secure if kept patched up to date). The only problem with ftp, and possibly sftp, is if you're both behind SOHO routers doing NAT (address translation), old style ftp clients may not be able to connect. Newer clients/servers allow restriction to specific ports so the NAT isn't a problem. Regardless, you're likely going to have to forward some ports on your router. If it's a windows machine, remote desktop is probably easiest (provided it's not a "home" version of windows, as they don't support full remote desktop via remote). VNC is reasonably secure; if you're worried about security, tunnel VNC over an ssh connection (OpenSSH or putty's ssh stuff). Of course, that requires more reading, and more time figuring out stuff, so I personally wouldn't bother, unless it was like a work shell that I was using 8 hours a day. There's another VNC like deal the name of which escapes me. (I haven't done any of this in a few years.) I'm using FileZilla ftp client, but I know it's got a server too, and it's very popular. I don't know how it works with the NAT problem mentioned, but I suspect they've got it squared, because everybody is behind NAT these days.
More than that, I'd have to research. Which I don't mind doing, but won't do unless asked.
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