Sejanus.Aelianus
Veteran
This is what is most important to me. I plan on working on my home PC remotely. I wouldn't get a tablet/chromebook/netbook JUST to browse the web/ play with apps.
I don't plan on doing any serious work either. Just some casual work every now and then. Like to check up on some things at work and/or to do some quick touchups in photoshop.
There's an awful lot of misinformation flying around this thread. What you wish to do is relatively simple and can be done with strong security.
You need two pieces of software and both are free. First, you need to set up a VPN connection between your home computer and your Chromebook, netbook or whatever. This provides you with a secure channel that is, for practical purposes, too difficult for an outsider to break into.
Then you need to set up a remote desktop session over that VPN connection, using any one of the various tools you can find via a web search. VNC is the preferred tool, because it's been around for a long time and is open source but there are various new ones levering some of Google Chrome's facilities. If you did want to use Windows, there's a built in screen sharing system (Remote Desktop). Apple also has a built in app called, oddly enough, Screen Sharing.
There's a bit of learning to do but it isn't beyond anyone who can follow instructions.
Best of luck.