If you're not wanting to do full-screen or 3D gaming, then VNC or RDP or screencasting will probably fit the bill. It will work best where there is very little happening on screen - you'll probably get up to 1/2 - 4 FPS depending on WiFi and how much is being updated on the screen.
VNC and RDP will give you a crisp, pixel-for-pixel picture that is pretty close to real-time, and are generally pretty light on resources. There are a multitude of clients for iOS devices; windows comes with an RDP server (look up how to enable Remote Desktop Connection), and I believe TightVNC and UltraVNC are two free VNC servers which are pretty popular.
Screencasting (such as with Join.Me or Livestream) actually generate streaming video - you can get much higher FPS with this method, but it is extremely processor intensive (you're encoding video in real-time) and there is also a second or more of delay. Any fine text will probably not be readable because the output resolution will be fairly low.