Repairing leaky, rusty water spigot

[clkingtx]

Hello,

I am trying to figure out if this is something I can do myself, or if I will just cause more harm by even trying. Our backyard spigot is really leaky. My hubby can shut it off, but with arthritis in my hands, I can't grip it well enough, and it leaks until he gets home and turns it off. We just moved here in January, and there have been many things to repair, and we both would rather do it ourselves whenever possible. I am fairly capable with tools, and feel like I could probably take it on. I have found some videos, but none that have the same kind of faucet(usually if I can find a video I can copy it). I tried to unscrew the screw on the handle, but it is stripped out. Here are some pictures. I know a lot of you are skilled diyers, and I would REALLY appreciate any advice.

Thanks!
Carrie