You can do this a few different ways (p.s. should be like a 4.10 if your a manual 4 cyl)
1) See if you can get your build sheet, might not be able to as it may only work for 98 and up
https://wranglertjforum.com/threads/how-can-i-find-the-build-sheet-for-my-jeep-wrangler-tj.3838/
2) roll under it and see if the tag is still on it to identify
3) jack it up, pull the cover and read the gear
4) jack it up, hold one tire and spin the other, count how many times the pinion goes around for one revolution of the tire
Do the math (people will argue with this, but this is the math)
(New tire size/Old tire size)* current gear ratio = new ratio
factory tire size on your jeep should have been like a 215 or 225/75r15, so 27.5ish, and if we assume you have 4.10s should look like this
(31/27.5)*4.10= 4.62, so a 4.56 or a 4.88 would be a good choice (remember this is an example, check what gears you have first, some early 4cyl got 3.73, and some magic ones had factory 4.56)
Not gunna give you dollars and cents here, because there's to many variables, but at least here's guide line.
https://www.quadratec.com/p/yukon-g...ERBAkLkwwjFhQatJIBSkZbsH4ZRX8EAhoCFhEQAvD_BwE
that is an example of most of what you would need, one thing to note here is that if you are for whatever reason have like a 3.55, you will need new carriers as well.
assume that the shop will be paying near that price for the parts, and obviously aren't just going to trade dollars with you, they need to mark it up, probably in the range of 25-50%
labor will range (this is for both axles) from about 5 hours on the low end to 10 on the very high end, last I heard rates in Yakima were around 100 an hour, may be more.
add tax, and that will give you an idea
Hope that helps