Internet bridge from house to shop.

That would work well. They claim 300mbps which is most likely fast enough for internet browsing and even watching movies

If you can get higher speed and more throughput the better.

The 120v adapters I noted work the same way except it's wired through your ac system
I still have not ruled out pulling a cat5 across the yard.
It is so dang rocky it looks like a battle field when you start digging.