Yikes! Without knowing specifically which lenses it's hard to know what to recommend. It's also beneficial to you to describe your expectations for the system. (How you might use the system and what you are comparing to.)
I also have a Sony a6000 body but I don't have a Nikon/NEX adapter (yet), so I can only relate my research regarding that combination, plus my experience with an EOS-EF/NEX adapter. (Plus a limited experience with Pentax M42/NEX and Pentax PK/NEX adapters.)
For autofocus Canon EF mount lenses, I am using a "Commlite Autofocus Adapter EF-NEX". Since this adapter supports some electronic connection and functions, I had hoped that it might be useful to leverage my collection of EF mount lenses (including Canon "L", Sigma "EX"). Sadly, while the Commlite adapter got better user reviews than the Metabones adapter, which was the closest competitor, AF speed is sad. AF accuracy was OK, except indoors and low-light outdoors when the AF typically would not lock. Aperture control worked well.
From this page: http://briansmith.com/nikon-lens-adapters-sony-e-mount-cameras/, Brian Smith suggests that Nikon AF is no better than my experience with Canon AF, so a Nikon AF-S "G" series lens is just going to be frustrating. He gives his individual experience with popular Nikon/NEX adapters on that page.
For manual lenses, when you have time to carefully manual focus and manually set aperture, the experience is very much like the old "preset" lenses of old. In other words, you can get the job done but you don't get much assistance from the camera. It's best to just use the a6000 in full manual mode and with an external exposure meter. Focus can be helped with the a6000 Live View and magnified.
My honest opinion is that if you have a decent set of Nikon "F" mount lenses and you want good productivity, it's best to stay with a good Nikon camera body. I use the Nikon D7200 body with my AF-S, AF-D and even old AI manual lenses, and it's a pretty rewarding experience. I'm probably not going to get a Nikon F/NEX adapter for my a6000 because it really doesn't gain me anything.
BTW, if you want to test your lenses on your a6000 body I believe that a few lens rental places do have an appropriate adapter to rent inexpensively.