Thanks for all your help guys! The Edelbrock 1805 makes her purr! Easy install and for an engine that hasn't been turned over in around 6 years, runs damn smooth! Replaced the fuel filter, fuel and vacuum lines as well...

The first issue I have is when I shut down, the engine still sputters for a few seconds after I turn the ignition off, and some discharged fuel spits out of the top of the carb (I haven't run it with the air cleaner on yet)

Second - The transmission won't catch. Park catches just fine, but the gears only softly click with the shifter (Hurst Dual Gate), but coasts like its in neutral in all gears, and on both sides of the gearbox. No normal gear clicking coming from the tranny when I shift either.

My uncle told me a shift kit was installed before he bought it (he believes it runs off of hydraulics)... Any ideas at what I can look for?

 

ok thats good! first it sounds like the carb is running rich what does the exhaust look/smell like? second is the shifter hooked up you would feel it and hear it shifting. third a shift kit is a series of valves and check ***** inside of the transmission so yes it is hydraulic.

 

Ignition timing being off can cause the carb to spit at shut down, check that with a timing light.
Park isn't a gear, it's a mechanical pin through a drum. The gears work by hydraulic fluid pressure. Is the fluid level in the trans up to where it's supposed to be? Run the trans up and down between reverse and drive a few times (assuming the linkage is hooked up), put it in park, then check the level.

 

Yes, timing, and fluid level in the trans! Do the easy/cheap stuff first! Be sure the engine is warmed up prior to checking the timing, so it will idle well. Same for the trans; check it warm.

 

He mentioned to check the linkage... How would I go about this? I have ZERO transmission experience. A quick search, I get the basic understanding but unsure of where to look on my car and what issues a trained eye would notice. Any guidance would be appreciated!

 

Need to jack the car up and get under it. Check visually at the linkage connection arm on the transmission for any worn or sloppy connections. If you can get someone to wiggle the shifter forward and back as you watch, you might see any slop in the working points. If all is OK, then disconnect the end at the arm, and manually click the arm through each position, to see that the detents can be felt in each position. Finish by putting the transmission arm in neutral, and then put the shifter also in neutral, and check to see that the end attachment goes on the arm easily, without having to move it forward or back. If it wont go on, then adjust so it easily drops into place with trans and shifter both in neutral.