What parts are essential to replace when doing the throwout bearing?

@Boomer453 - apologies if you already know these things.
Keep track of where your bolts go-there are some different sizes and some unbolt in different directions, and some seem to be hidden.
Pro tip: Get a piece of cardboard, roughly draw your tranny on it, w/ an "up" arrow, doesn't have to be the same size. As you take bolts off, poke them through the cardboard in the same relation to the tranny so you know which one goes where when you put it all back.
 
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I wouldn’t use a chisel separating, but that’s just me.

mid you have the bolts free (there are some coming front to back holding the sheet metal dust shield) if they are all off, just shaking back and forth should walk it out no issues.
I hooked one hook of a come along onto my rear bumper hitch and the other to the tranny...popped it right out
 
A bit late, but this video describes why 6sp make that tra-ta-ta-ta-ta-ta noise. Take care of it while you there.
As far as Timken tob, have you checked it? mine literally fell apart when i took it out of the box.
My Jeep was sitting on jack stands for a week, cause Amazon kept sending me some Timken and National factory reject tob.


 
Didn't read all the replies so I apologize if I am repeating what was previously said.

I suggest getting some long bolts which are the same size as the transmission to bellhousing bolts and cutting the heads off. Thread them into the bolt holes and it will make life much easier to get the transmission into place. I'm not sure how heavy the Jeep transmission is but I have had the transmission out several times in Fords and was always able to muscle it in and out without a transmission jack, even the heavier cast iron housing Ford toploader.

Good luck!