What's the easiest way to tell which axles I've got on my TJ and what my gear ratio is?

If it is not a rubicon you have a D30 front. Your rear axle could be a D35 or D44.
Easy way to tell on the rear axle is check the fill plug... if it has a rubber/plastic plug on the diff cover it is a D35, if the diff cover has a metal fill plug it is a D44.

To find your gear ratio, look on the rear diff cover. On the left side of the cover there should be a metal tag held on by one or two of the cover bolts. The gear ratio will be stamped on the tag. 3.07, 3.73, and so on.

EXP.....



This is all IF the axles are the factory axles. But from the pic's of your new TJ. I'm betting there stock.

Careful on IDing all none rubicon's as d30's. If anyone purchases a tj today they are used tj's and previous owner could have swapped it out for a D44 or something else. Dealership for instance rarely know or care what is under the vehicle. My wife bought a beetle a few years back she asked if it was a turbo they said NO she got home popped the hood and YES it was a turbo.

chiro, thats a nice steal thats why you look at something before you buy it.. The difference between a turbo vs non turbo is very easy to see, feel, or even hear.