i teach economics at the university level, and i have a lenovo x200. it is way outside the $1000 range. it has a wacom screen and the stylus is very precise (we do lots of crazy math too ya know). my normal computer is a mac, but i LOVE this thing. lightweight, LONG battery life (5hrs easily), and very sturdy construction. its currently running vista and i've had no problems (core 2 duo 2.0, 4gb ram)
i'd either save up (or convince them to give you more money - if your university is in the US and receives perkins funding, you might go that route. as long as you teach perkins eligible students, your grant administrator can probably find the cash (it might take bribing them with chocolate though..lol)) or, if there is a PC in the room invest in a wireless/bluetooth tablet that you can just carry to the classroom with you. you are going to have a hella-hard time finding all that you need for less than $1500 (unless you go used - our university wont buy used), and one of those cheap ones will just fall apart. one of my colleagues got one of the $1000 HP offerings and HATES it. a year later, the screen flickers, the battery sucks, and the tablet is not very sensitive.