There's tons of info out there, but in general, you need to address a few items. From the fact that you are asking the question, I'm going to steer you towards the "Easy button" approach, not the hardcore budget build:
Fuel system - Likely the best way is to essentially get the fuel system from an '87 TBI truck, but with a higher pressure pump. New tank, run lines as appropriate for your skill/budget/existing condition level, and make sure you have the appropriate regulator, probably a "returnless" system on the LS3 that can use a QUALITY "Corvette" filter/regulator, or get standalone aftermarket filters and regulator, then get it all connected together.
Wiring - Buy a harness from a reputable vendor, or do your homework on how to cut/splice/modify one you already have. I'd suggest getting a factory PCM with it if you don't have one. The Holley stuff seems Sexy, but my opinion is that factory is better for 90% of swaps out there, but get your harness/tune/computer if needed from a good, reputable source.
Mounts - I'd say you have 2 options - Leave your transmission in place and buy a set of adjustable/slider mounts from someone like ICT or Dirty Dingo and run no AC or a high mount/aftermarket AC, or get the Tejas mounts, use the factory AC compressor, and use the chance to upgrade your driveshafts as your transmission will move forward a few inches.
Alternatively, you would possibly be able to leave your transfer case in place, but swap your TH400 for a 4L80e with the Tejas mounts. Read up on Tejas's site or call them, he's a good guy with lots of info.
AC - See above, either run the factory LS3 compressor, or get a Sanden of the appropriate style. The old compressors from our trucks are not that great, and the hoses need to be replaced anyway.
Transmission - If you keep the TH400, get a spacer to go between the flexplate and the torque converter. There is a 6-bolt spacer, or just a little stepped donut. Either one should be fine. You may need to "adjust" some flexplate holes to line up, the old ones are on an SAE circle and the new ones are Metric, so the holes may be a hair off. A die grinder can fix it easily, or any number of folks will happily take your money and send you a new plate with plenty of holes in it.
Gauges - Keeping your TH400 simplifies the speedometer, but your tuner may need a VSS. Going 4L80e might help that situation if you do it right, and keep your speedo cable on the T-case, or you may do a 4L80 with the right T case to keep passenger side drop and get a VSS, but need a digital speedometer. Your tuner may have more info, and/or do some digging about using a 2WD 4L80e for the VSS in the case. Other gauges can generally be done with the factory sender on an adapter to mate to the LS engine. Info is out there, and it depends on what exactly you have or need. And of course, a full digital dash is always an option if you want that.
Hope that gets you going!
