Buy a used 15" MacBook Pro.
The used market shifts quickly, but right now there's a Mid 2010 15" with 8GB RAM and a 256GB SSD on eBay for $499, buy-it-now. Preserved for posterity when the eBay page goes down.
Worst case, buy one with a normal HDD and install an SSD yourself. It's not that hard, and you can use any standard SSD. Plus, you now have an external HDD for use as a Time Machine backup.
- decent 15" screen, meaning good viewing angles, good colors as high of a resolution as that amount of money can buy
15" non-Retina Pros have a 1440x900 IPS (high viewing angles) display, and can run an external display or two without a hitch. I use my 13" on my desk every day, the quality is comparable to my Dell U2515H. It's also bright enough to be used on its own.
Apple makes the most usable trackpads I've ever touched. I haven't used a mouse in weeks; I use the trackpad on my 13" Pro and my external Magic Trackpad 2 (same technology). No one comes close in terms of feel and usability - even simple things like thumb/palm rejection are implemented flawlessy.
You shouldn't have any problems staying well within your $800 budget, especially if you're not looking for newer hardware (which you don't need for the tasks you mention, a 2009 Pro would blow those out of the water).
They're made of aluminum, a.k.a. they're built like a tank. It's hard to actually damage one to the point you would notice it in daily use. I dropped (flung, actually) a 2009 13" Pro from a backpack about five feet in the air. It flew across the room, squarely hitting the corner a steel shelving unit. It left a nice dent in the casing, and I thought the edge-to-edge glass would be broken... nope, the casing absorbed the impact. That's a tiny dent, especially considering the forces involved. Another picture.
A common argument against Apple machines is that they're 'too expensive' - actually, they're cheaper to own over their lifetime when you take into account resale value (which Apple laptops hold, and no other laptops do).