Just remember if you go the WISP direction that you want to still have a different AP provide your own network's WiFi. Sharing your WiFi and connecting in WISP is too taxing on the radio to handle as it is dealing with relaying between two networks which requires a feat that is hard to do without a dedicated radio for each network.
Your best solution would be getting/configuring a wireless bridge device. These are designed to do exactly what you are trying to do. These are sometimes referred to as a wifi game bridge (they were origionally marketed to get things like the PS2 and Gamecube which had network ports/add-ons but no WiFi cards, to be able to connect to a WiFi network, but were also useful for printers and other devices). Any WiFi router capable of running DD-WRT firmware can perform this by simply changing the mode to "bridge mode". Some of those DD-WRT capable routers can also be setup as your own router as well without performance loss if it has multiple radios. I have owned 2 that had 2 separate 2.4GHz radios so that you could separate out older legacy devices (b/g or b/g/n from the ac devices so that your fast devices are not slowed down as your network is only as fast as the slowest protocol device connected to it).