The Nikon FT-1 adapter allows you to put F-mount lenses on Nikon 1 cameras. When it comes to using Nikon brand lenses on the adapter, there is an official list of compatibility from Nikon.
However, when it comes to using third party lenses, there is no official list or support from Nikon. To help you decide which lens to get for using with the Nikon FT-1, I have made a list of lenses from Sigma and Tamron, describing how they work on Nikon 1 cameras. This was tested using the Nikon FT-1 with firmware 1.2, and the Nikon 1 V3 with firmware 1.1. Future firmware versions may yield other results.
About the results: I first describe if the lens works on the FT-1. A "no" here means that you cannot use the lens at all on the adapter. The camera repeatedly shows a message saying "check the lens", and there is a clicking sound from the lens. You can not even use the lens for manual focus. You can, however, mount the lens using a dumb adapter without any electronic contacts at all.