As other folks have described, this is pretty much the way to go about it.
Have a bucket of warm clean water on hand with Towel, a good All Purpose Cleaner (I typically use Zep Citrus at 1:1 ratio) and a couple soft brushes to agitate the cleaner to break-loosen caked greases-oils at hinges.
A couple of soft small paint brushes can work well. I typically do one Jamb at a time, squirt product on, let sit 5 minutes, then go to work. I simply use a garden hose with 7 pattern spray, and use a shower setting.
With the Trigger on the sprayer, you can control the amount of water flow.
Repeat if necessary until all traces of dirts, and greases are gone. It takes time, but is not hard, let the APC do the work. Often on the Tahoes, there is a weatherstrip rail that runs the body length, this can usually be simply slipped off, cleaned, dried, and treated with a rubber treatment.
Usually, and considering the age of your vehicle, perhaps the only places that might need some polishing attention will be the rocker-sill panels which get scratched-scuffed by shoes entering-exiting the vehicle.
For these areas, a polish, and perhaps even a clear coat safe liquid compound can be used to bring back some shine, and help remove damage.
Continue on to all other doors, and don't forget the tailgate, probably the dirtiest, and the hardest of al Jambs to clean-detail.
I commonly disconnect the battery when doing this, as I might have the doors open for a few hour's time.
Dry all jambs with a towel, and warm clear water, leave doors all open to let fully dry.
The coolest product I have been using for protection, and gloss in these areas has been Ultima Paint Guard Plus. This is a Poly wipe on walk away sealant which will have your Jambs looking like wet glass.
Other Wipe On Walk Away Sealants such as Optimum Opti-Seal, Wolfgang Liquid Seal, Blackfire Crystal Seal, and other similar products work very nicely, and just as easy-well for this task.
I apply liberally, to insure very good coverage, let dry a good hour or so, and because of liberal application, one will probably see a little bit of hazing, and streaking. Simply go back with a clean MF towel, and buff-wipe all jambs to remove any excess product.
You'll find these WOWA sealants won't be leaving any dusts, or powders like typical waxes-sealants will leave behind. This will make the protective process of the jambs a breeze.
Do the final rubber-plastic trim treatment with good protectants, and products like WG Exterior Trim Sealant (WETS), Ultima Trim Tire Guard (UTTG) will work well.
Remember to relube all hinges with a good oil. I simply use good motor oil in a Oil Can with Flexible Hose to get into all the tight areas. Wipe away excess Oil with paper towels, and you are done!
Mark