New HDD or SSD in MacBook with failed hard drive?
As far as "worth" that is very subjective. The choice given is between a fast SSD drive (but smaller) and a larger HD (but 2x the size). So, it really depends on whether you need more space, or more speed.
Factually, the SSD drive is much much faster and will make your computer seem a lot faster - startup, app opening, file opening, etc. Almost like a whole new computer.

Can you do it yourself? If you are not afraid of using some small screwdrivers, sure you can. It requires some really small jeweler screw drivers, a plastic "spudger" or small plastic tool to unlodge a connector or 2. Some of the connectors are really small, so you have to be very careful to not force them. But it's not anything normal humans can't do. Here's a link with some sbs instructions.

https://www.ifixit.com/Guide/MacBook+Pro+13-Inch+Unibody+Mid+2012+Hard+Drive+Replacement/10378