Ok, I'm not familiar with any of those trails so I had to look them up on YouTube to see what they are like. There was a video of a stock GMT400 on a couple little ledges on the Maze Overlook and I think with a little work, your Suburban will do great for you.
My thoughts on it are this:
Do the budget lift I was talking about earlier. Probably use an actual add-a-leaf if you plan on trailering as it will also up your capacity a touch in the rear. I wouldn't try to go very big on lift, about 1.5" at most in front, let the rear go where it wants with a 2" AAL. Then you'll want the better shocks as well. 4600 Bil's should do good for you.
For tires, some nice A-T like BFG KO2s in 285/75/16 on stock wheels. There are a few companies that make tire and jerry can carrier rear bumpers for these vehicles with good protection and an integrated hitch that'll gain you some departure angle.
You'll probably want to eventually invest in a front bumper capable of holding a 12k or 15k winch. You'll want enough to extract the Burb then turn around and be able to winch your trailer out if it's hung as well.
I would consider finding a rear axle from a light duty K2500 from the mid 90's. It'll be a semi-float 14b with six lug axles so your factory wheels will fit. It's worlds stronger than your current 10b rear and will stand the strain of towing an off-road trailer. You should be able to sell your 10b easy enough if you have a bit of patience. The front should be fine if you can get a 14b that matches the ratio you have, which I'm pretty certain would be 3.73. It is the more common of the ratios. You might consider adding an ARB to the rear while you are in it. Then you can get the mid-range ARB compressor and have on board air as well as a rear locker should you need it. That's a good chunk of change that you can hold off on till you see if you NEED it though, but I probably would if I was building it myself. That's my opinion though, go with what you feel good about.
Your Burb is a 95, so I'm not sure if you have the TBI 350 or the Vortec 350. Either way, you need to get your entire coolant system flushed now if you haven't already. The OE Dexcool attacks aluminum if it's over 7 years old. I've seen it eat intakes till they start leaking. If you have the Vortec engine, you need to find out if the intake gaskets have been changed yet. These engines are bad about breaking the intake gaskets and filling the cylinders with coolant. It's happened to both my 99 Suburban (cost me an engine) and my 00 K2500 (caught it right as it started).
You should also have the transmission fluid changed (not flushed) and the shift solenoids replaced with OE (AC Delco from a Chevy dealer) ones before one of them costs you your transmission (again, killed the trans in my 99 Burb). These are common issues with the 4L60E transmisson and because of the way they work in conjunction with each other, losing just one basically cripples the transmission.
I know those seem like major issues, but they really aren't. Every vehicle has it's weaknesses. My Xterra came to me with a new transmission after a common issue with them killed it. I also had to have timing chain tensioners done because of a factory defect. You have the Suburban and from what I saw of the trails in the videos, you'll do fine on them in it, even with a trailer, after you get the experience behind the wheel and know your truck.
