So I just bought a 96 formula 116k for 850 good deal in my mind but the transmission Has a problem with it when it starts cold it goes into gear but after it warms up after about 10 mins it no longer goes into gear are we talking rebuild or replace or just a part

 

Most likely rebuild, but you can check the line pressure to see if it is low.

 

Thank you I was going to take it to a local shop as well

 

If after you turn it off and et it sit 10- 15 minutes and restart it the filter is probably block but of course this would be an indication of internal failure. Sounds like your going to need a trans

 

I got quoted 1600 by a local shop he said it could be the 3rd and 4th gear problem from what I told him does that sound right

 

That is a reasonable price if it includes removing, rebuilding and re-installing the trans. The notorious 3/4 clutch definitely sounds like it is shot.
I would ask the shop to rebuild it using a 4L65E rebuild kit as it includes a better 7-friction 3/4 clutch and that is the only difference. (In other words a 4L65E rebuild kit can be used in place of a 4L60E rebuild kit.) Also have them install the Sonnax 4L60E-LB1 boost valve which will increase line pressure across the board to tighten up shifts and actually reduce wear on the frictions.
If the shop doesn't understand how to do that, find another shop.
(My local shop has a big stack of the Sonnax boost valves and installs them when doing a "stock" 4L60E rebuild for any sporty car.) The shop can order the Sonnax boost valve for their distributor, e.g. Transtar.

 

Who sells the 4L65E rebuild kit? I'm looking to do a rebuild soon myself.