Re-gearing an H3 (other than 4.10s or 4.56s) is a major undertaking. There are plenty of options for the rear diff...its been around for 30 years or so. But, the front diff is very small and a relative new-comer, and there is not really any options for re-gearing it (other than what the factory offers). Since both axles need to have matching gear ratios, the lack of front axle gearing options is what the real problem is. Even if lower gears were available for the front axle, I would not recommend them do to the very small ring gear diameter and the hefty 5500lb anchor it needs to move. I'm running 5.13s and 37" tires but, this requires a complete front axle swap. I chose a solid axle from a 70s-era chevy truck, and like the stock H3 rear axle...there are plenty of gearing options available for it. Unfortunately...this type of swap is neither cheap or easy compared to a simple gear change.
As far as performance? I will flat-out destroy a stock 5-cyl H3 in a drag race. Its hard to describe the difference lower gears make...but they basically put the RPM range of the motor back to where it needs to be. The 5-cyl likes to rev and it doesn't have much low-end grunt, so gearing is more critical than it is on traditional V8-powered trucks. Not only is cruising RPM raised back close to stock...but the shift points come fast and hard. Most of us run 35" tires and they really make the 5-cyl. struggle, especially on the highway. Its not the weight or the width of the tires...its the larger diameter that is reducing your effective gear ratio. Its amazing how much we H3 owners get used to lugging around our H3's with big tires. We bolt em on, and we're so impressed with the extra ground clearance and aggressive looks...that over time we just get used to it. But if you want a reminder to see what you're missing...just bolt your stock tires back on! Usually it hits you like sledge-hammer how much power those big tires are costing you! Ultimately...the goal is to get all the benefits of larger tires, without sacrificing the power & torque it takes to drive them. And unfortunately for the H3...there are no options to do this without dropping $5000 to $10,000 for an axle swap. So for now...you're stuck with a Cold-Air Intake, a computer tune, and maybe a header/exhaust system. BTW I would never attempt to add a super or turbo charger to a GM 5-cylinder...that's just silly.
As far as MPG upgrade? I'll just pretend I didn't see that.