Sellers always think their stuff is worth more than it is. They'll quote things like 'oh, but it's the last upgradeable Mac' and talk it up, but I guarantee they'll be looking to buy a Retina MacBook Pro with the money they make from the sale (and with a student discount applied, they'd easily be able to buy a new model from the money they're selling that for).
MacBook Pro 13" isn't the 2013 model, it's worth remembering that the base MacBook Pro hasn't been updated since 2012. The deal is fairly competitive but again not great.
In all honesty if you're looking to sink $800 on a Mac, you might as well eek a little extra and go for a new Retina MacBook Pro, or a MacBook Air if you're on a budget. If you're a higher-education student as well, you'll get 15% off RRP, so that's worth considering. Failing that, refurb models on the Apple Store are really competitively priced and always of the highest quality (plus you can purchase AppleCare for them).
If you buy an out-of-warranty Mac, it's going to cost a good $300 if either the display or Logic Board breaks. Worth adding up the pros and cons and remembering just how expensive this could be. Personally I couldn't buy a Mac without the security of AppleCare, unless it's too cheap to resist, or it's an older model that I'm looking to teardown/run legacy software on.