4.88 vs 5.13
 

So first off I know next to nothing about gears. I have a 2dr manual rubicon with the 3.6 and wanting to get everything done to run 37's. Now the type of driving I do is 3hrs to work once a month and then back, with a speed limit of 55 most of the way, a tiny bit of in town and then I do both blasting around fire roads, with my kids, and then more serious rocky trails when it's just me and my dog. So what are the real advantages if any on going one way or the other. And please don't say subjective things without explaining more. Also any recommendations on brands?

I have a 2014 JKU with 4.56 gears on 35's. I drive on the highway a lot. For me the 4.56 is almost too much gear for the highway. I'm turning about 2500 rpm at 70mph on the highway. Google "3.6 manual jk gear rpm" and you'll see a chart about gear ratios vs tire size and engine rpm at 70. If you don't get on the highway much having lower gears won't matter as much. If you have a 36" real size 37 then you'd be about 2540 rpm for 4.88 vs 2670 rpm for 5.13. Anything under 3000 rpm is ok on the highway to me but lower is better. Stock I was about 2000 rpm. Longer trips the droning gets annoying. Bottom line, If you don't mind the highway RPM, go 5.13. You're not going to regret a better crawl ration when you get on the rocks.

I run 4.88's on a 2 door manual with 37's, I think its the perfect gearing for a good mix of highway and trail use. RPM's aren't too high when cruising and I have all the power I need with the 4:1 Tcase in the rocks. If i was geared any higher I would be unhappy on the hwy.

Agree with Ajkaz above. With the Rubi TC, you should have zero concerns with offroad gearing, in which case focus on the pavement. I have 5.13s and 37s on a 3.6L, but it's an automatic. It's a bit aggressive for the pavement as I run 3k RPM at 75mph interstate speeds (pretty flat here in Texas, but with stiff headwinds), but I erred lower since I don't have a 4:1 TC. I do see you mention your highway driving is more like 55mph, so your RPMs won't be near as high (regardless of auto/manual), but I'd still say 4.88s will be plenty low to get the job done and keep you satisfied.

In regards to brands, you'll get varying opinions. You can't go wrong with Yukon, but it's harder to find a price break on em compared to G2 or some others. I'd venture to guess that you see more failures due to install error than due to brand of parts though.

Cool and what speed on the hwy? Cuz most of my hwy driving the speed limit is only 55. Also did it change your shifting much? And is the 4:1 Tcase something you added? Or is it stock? Mine is still pretty much bone stock Rubicon save for a spring swap. Sorry if its seems like an obvious question.

Non-rubicon tcases are 2.72:1
Rubicons come with a 4:1 tcase as standard equipment. (as well as a front d44 instead of a d30, selectable lockers, slightly beefier axle shafts, pretty 'I'm a Rubicon' badges, etc)

Cool thx i also dont exactly have a budget as i just figure out what i want to add and save up the money for it. So it makes it easier to just decide what i want instead of what i can afford or have to settle somewhere in between and yes i know that means ill probably never be satisfied and finished with it.

I've got a 3.6l 2-door manual Rubicon with a simple spring-swap lift as well!
I'm running 35s, and frankly, I can barely tell a difference from stock. With the lower gearing on the manual, the 4.10s do just dandy on the highway, even uphill (I usually stick to around 65, more because it gets uncomfortable quick without doors or a roof than for wanting power) and in low-range it's just baaaaarely stallable on the rocks, and that takes some doing. I cannot keep up with other Jeeps between obstacles if the TC is in low.
Obviously with 37s your experience will differ, but you may want to just stick the bigger tires on there first. You may decide you don't even need to regear.

Are you installing yourself, or going to a shop? I don't know how much things have changed over the years, but for a long while most of the 'JK' gears were coming out of the same place in Asia and just boxed for the different mfg's. (I'm sure they each had their own specs and guidelines to be followed, but I don't think we've seen a lot of feedback indicating that brand A is any better or worse than brand B.)

If you are paying someone else to install, check on not only the prices and warranties, but how those policies might change if you supply the parts. Even if you decide you want a certain brand of gears, you could be better off with what that particular shop has past success with if it comes to a warranty/repair situation.

Going to a shop for sure cuz I've never done anything on a diff other than a fluid change, and there's only 1 local shop and they said they will install whatever I want as long as supply the gears, but had no recommendations for a Jeep as they mostly deal with trucks.