no, this one will still be within Apple's update range for the next 3 or 4 years, worst that could be happen is the keyboard breaks down as this series had bad keyboard design but they got sued in Europe for it and they'll repair it regardless of warranty if it happens
Keyboard Service Program for MacBook, MacBook Air, and MacBook Pro
support.apple.com
software wise is still good to use, I use a 2012 iMac and it's still within the updates range, so with your light browsing use you'll be fine with it
my only objection would be how much you'll pay for it compared to getting a new one and the lower resolution these have, I know a girl that has this very exact model and it's alright