a proxy server that someone installs

Similar to a proxy in that they are used to hide your identity, except all information actually passes through the Wingate, if you have a slow Wingate you get slow download/upload speeds. Wingates are also used to force FXP transfer on pubs that do not normally accept FXP, again all data passes through the Wingate so you need one that is fast for it to be useful.

a good bugget-minded business hotel chain with good amenities

a windows-based computer that can be used as a gateway to other computers