- Easiest: get yourself a good laptop and use that, nowadays laptops can be just as powerful as a desktop. You can sync certain stuff between your desktop and the laptop too if need be (if you wish to work on the same file/project on more than one computer).
- Remotely connect to the computer you need to use that you do not have physical access to at that time.
As for purchasing software, you will need to purchase at least a license to use the software on a specific computer. Many software companies offer licenses for more than one computer. No way arround that, unless you limit the amount of computers you use for the same to 1.
If the only thing you need to have access to anywhere are files/documents, you can use something like:
SkyDrive
Foldershare (beta)
Office Live Workspace (beta)
Live Mesh (tech preview, limited beta)