The car looks like it's in pretty good shape. I hope someday I'll be able to do something like that with my family. As Bullydawg said, it's a great learning opportunity for everyone and will teach you all a thing or two about cars.
Check out UFBA.Org if you get the chance, is the Utah F-Body club. They've got events and stuff going on throughout the summer and they always are ready with info if you ask.
Anyway, all in all, like i said, it looks pretty good. The stick shift you're referring to as "unknown" appears to be stock from the picture. Your steering wheel is not stock. Also, I'm not sure what part of Utah you're in but if you're up here in Davis or Weber counties you'll need to get all the correct smog equipment unless you can prove that your car didn't come with any which will be hard to do. There's alot that goes into that though so I'd recommend not doing it unless you have to. Trust me, on mine, it's a ROYAL PAIN THE ....yeah, you get it. haha Anyway, good luck on the project and let me know if you have any questions. I've done alot of work to my 84 and I've loved every minute of it.
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1984 Pontiac Trans AM
350 4-bolt main bored .040
Sportsman II Heads, Pro Magnum Roller Rockers, Lunati Voodoo Cam
Hooker Headers, Custom Catback with Hooker Aerochamber muffler
700R4
3.73 Factory Gears
My 84 Trans Am <-- Oh, click me! Click me!
My 67 Camaro <-- Or me! Or me!
"Life is tough. It's tougher when your stupid!" (John Wayne) Freedom Is Never Free! 
