What desktop PC should I be looking for?

I am looking for a PC to use at home and to do a little bit of work stuff as well (I am a teacher). I also like to play on-line backgammon.

I am thinking along the lines of a 24–27” screen, 8GB and 1TB, Windows 8. I would like to keep within $700 budget. What else is important that I look for?

There is some technical stuff that I don’t really understand such as what kind of processor is better (AMD A6–5200, AMD E2–3800, AMD quad-core A4–5000, dual core??). And what is 10/100 ethernet?

I would also like some info on:
Is Windows 8.1 better than Windows 8?
Is a touch screen worth getting on a desktop? (I was thinking about having the screen like an arm’s distance away)
What is better in terms of brands—P, Lenovo, Dell, Acer (I’m not a Mac person)?
What store has the best prices?

Thanks in advance for all your advice and suggestions.