Different brand shifters
It won't work. The two systems have different cable pulls. 

Buy a SRAM (or Friction) shifter if you want to use the SRAM derailleur or buy a Shimano derailleur. 

Either option is about the same cost (though if one is cheaper, the Shimano derailleur will probably be the cheaper one). You just need a 7-9 speed Shimano derailleur with sufficient capacity and cog sizes -- the Altus M-310 8 speed derailleur looks to be about 16 USD at the moment, which is probably adequate.