Use an Access Point cabled to your existing Router would be best. (And a Wireless Card for the Computer) Depending on the location of the AP in your house and what obstacles are in the way, it may work well. I'd position the Access Point in a direct line of sight to your shop for best results.
Outside, with a clear shot, Wireless can be good for 1000 ft. Inside you're lucky to get 300 ft.
It mainly depends on what is in the path of the signal.
The signal goes in all directions but if you can give it a clear path it works best.
brad

