Welcome to the wonderful world of Virtual Network Computing/Computers, or VNC. Please take a moment if you have not done so already and read our FAQ on Vine/VNC.
With VNC server installed on your home computer, you will be able to connect from your remote office (1/2 mile away) using wifi and VNC technology and see your Home computer desktop. With OS X 10.4 and above you will be able to right click and copy items in the remote connection window. You will then be able to right click on your local desktop and paste items. This will start a remote copy process to your local machine. Please note however that for changes you make to be made to the original documents at your home, you will need to copy back the files you have changed.
Since it sounds like you want to run spreadsheets and word documents with Excel or Word on your computer at Home, while you are up at the 1/2 mile away office (via wifi and VNC), it will indeed be as if you were sitting down at the Home computer working. In the connection window, you will see your desktop, all the folders, files, application/file dock, and desktop image/s of your Home machine. You will be directly connected to your home computer, with the desktop and windows seen as if you were right there. You’ll be able to launch apps, drag folders, make new folders, organize files, read email, open excel documents all on that home (remote to you since you are up in the 1/2 mile away office/studio) computer.
I can’t really speak for Bill Gates, however using VNC is perfectly legal to do as long as you are using it with software you legally own and have purchased. Please look shareware or freeware if these terms apply.
You most certainly can run remote applications like email clients (OS X Mail.app), so you will be definitely able to read your emails on that remote (home) machine from your studio, just as if you were sitting at home.
I’m not sure there is really an A-B comparision that is simple enough for an experienced user or newbie alike to digest in one sitting. However, there are documents online at Apple about ARD. And there are documents online about VNC (client and server). Both cover details about each technology. Fundamentally ARD and VNC both do about the same thing for a majority of users (which are much like you). However, ARD is expensive, about 500 USD to administer and use the ARD technology. VNC Server is FREE, and the Redstone Software VNC Client as of this writing is $29.95, has full support and is very well respected in reviews and around the globe by thousands of users. So, to summarize, Vine VNC is a great value and price, and ARD is just flat out pricey. That’s how I would compare the two. Disclaimer: I used Vine VNC daily, enjoy its simplicity. I also work for Redstone Software as the QA/Support Manager.