no cost, its just has to be turned on. it is off by default since it is such a security risk.
some type of online storage would probably be the best option for a slower connection. you'd basically just be starting it remotely and when it finishes, uploading the results back to your storage.
it is easy to use really as it is just like sitting in front of the pc. you see the desktop, can use the pc as if you are sitting there, so nothing new to learn. you just control it from elsewhere. considering you are accessing it from what is essentially a public connection, you def want to use an encrypted connection to your house. i had a tutorial at one point that set up remote desktop and an encrypted connection. i'll see if i can find that link for you to check out. it was easy to follow and worked great using Putty to make the connection and authenticate using your pki key.
not the full pki set-up but this is the basics for turning on and basic security for RDP in windows
While there are many alternatives, Microsoft's Remote Desktop is a perfectly viable option for accessing other computers, but it has to be properly secured.
www.howtogeek.com
it is a lot more involved to use a pki key but this at least turns on encryption and limits who can log in to just a single user you will designate. as you can see it is not hard to do the basics