I'm very happy with the Avery kit. I deleted a few items that I already had and they still gave me the discount. Since then I have ordered several more times from Avery and also bought some things from Cleaveland.
I don't think you need to over think this, all of the tool suppliers you have mentioned are good choices.
I deleted the extra bucking bars and went with just the tungsten bar. Ended up picking up some similar steel bars at Harbor Freight for much less money, but I hardly ever use them. Definitely spring for the pneumatic rivet squeezer with adjustable set and multiple yokes. I already had some of the files, metal snips, pop riveter and safety glasses. Things to add to the order would be a single offset rivet set, tubing bender, snap-socs (rivet set caps), tank dimple dies, rivet removal tool, torque seal, boelube, rivet fan, oops rivet kit and extra consumables like the mini scotchbrite deburring wheels and maroon pads.