|250' can be done easily with Cat5e. The maximum segment length is around 380' (100 metres).|
You can also do this with wireless but you would likely need to buy two wireless antenna to do the job.
I doubt a wireless router would have a strong enough signal to reach through walls and across 250' so that's why I mentioned antenna's.
There are quite a few companies that make point-to-point wireless antenna's so you could easily research some of those via google to get an idea on price.
If it were me, I'd give serious thought to pulling a couple cables to the shop. If you buried them in some plastic conduit it could be done cheaply and would definitely be more reliable and give you much better bandwidth.