When pulling out in first gear my Chevy S-10 jerks really hard and makes a grinding sound until I completely release the clutch. Is it my transmission going out or something to do with my clutch?
I would guess your clutch release bearing is starting to fail. Get it checked and fixed if necessary before it causes any collateral damage. If it has enough play in it, it can wreck the gearbox driveshaft which can be expensive - i.e you have to recondition or replace the gearbox.
A simple diagnostic test: listen for noises when you press and release the clutch, with the car stationary, the gear lever in neutral, and the engine idling. Any sort of noise (squeaks, rattles, grinding noises, or whatever) means there is a problem somewhere.