I have a bunch of Kill Teams but my favorite are: Orks, Genestealer Cults and Chaos Space Marines. The spoiler has some pictures of them. I pretty much only play for fun with varying levels of optimized teams. I think Chaos Space Marines basically need Berserkers to make it an actual game outside cultist spam and getting a mission that favors hordes. However, some of the Kill Teams that I find fun while being a little harder for my opponent are probably my AdMech and Imperial Guard, and they both do well for the same reason lots of special/heavy weapons.
I don't know if I have a favorite weapon in Kill Team. I like the idea of a Chaos Space Marine with a Heavy Bolter but that doesn't really translate into anything special in the game other than a now wasted
CSM Gunner slot. I also like Power Fists in general, but they too are hard to hit with, overkill when they do and too many points to bother with. I guess my favorite weapon in Kill Team is the Ork Boy Rokkit Laucha. You can go all game not rolling a 6 to hit with them, but once you do it is all downhill to removing a model off the table. Probably my favorite effective weapon is plasma weapons. Granted, when playing
CSM, I like to state, "there is litterally no downside to over charging plasma." as I over charge to even kill hormagaunts.
I can even go over kill teams I don't like playing as much. I can't say I like playing Dark Eldar. I only have the core rulebook (Kabalites and Wytches) units, but I feel dirty playing them as they just seem mean when they do well or fold like a house of cards. I also don't much care for playing Necrons since I never completely know if I going to not play a new player, and they are so incredibly frustrating if you aren't prepared for Reanimation Protocols. I am split on Space Marines. I have a Primaris only
40k army of them that when I played them in Kill Team they are kinda boring. Conversely, I have a 30k Dark Angels/Fallen that allows me the more interesting Company Vet options, but doesn't have Primaris or Scouts available. So having my unit options split across two differing paint schemes (and I am not about to combine them) makes both teams feel kinda one dimensional.
As for rules, my group pretty much ignores the Scouting Phase. We found that booby traps is really the only good one and more often than not if that isn't the choice it is disarm booby traps so it is a kinda waste of time. I mean some factions can make better use than others, but still we sometimes forget it exists. The other rule we usually ignore is the falling after being hit and standing within 1" of a ledge. Taking the high ground is usually a bad idea anyways and no one does it so to add further risk means the battlefield may well not have additional levels. We also rarely make use of Reserves or Outflanking since the board is already small enough and has plenty of hiding spaces. The one rule I like to add is models that have the high ground (about 3" above) automatically gain cover. This usually the case according to the rules already, but I like to have it expressly stated. The other couple of rules are models standing in craters automatically have cover and Death World Forest terrain automatically blocks line of sight if passing through two or more pieces.
What keeps me coming back is the rules are fairly simple. Which is nice if you are like me who also play full
40k and Age of Sigmar as well. I think they work better than they do in full
40k or even Age of Sigmar. Combined with the fact that getting almost any faction for less than $100 US with a decent number of options means if a faction starts to get stale you can switch it for some else completely different easy.
