These are the items in the game that I think are the most important towards guaranteeing your success.
This is the best weapon you can ever have because you can get it no matter which playthrough this is for you, and it can kill zombies in one hit and take down Psychopaths in only a few swings. Now, because it's so strong, it can also take down your survivors real fast if you aren't careful. However, I always made sure I had at least one of these on hand. That's right, at least one. Every time you enter Wonderland Plaza after defeating Adam, one of these will spawn for you, so you can grab as many as you want. Don't be caught without one!
Very critical to your success with the Mini Chainsaw are 3 books. These are found in two places and should be picked up as soon as you start the game. First off, in the bookstore in Paradise Plaza is an Entertainment book along with an Engineering book. The last book is in Wonderland Plaza, in Sir Book-a-lot, and it is a Criminology book. All 3 of these books will up the durability of your Mini Chainsaws, totaling it to last about 27 times longer. You'll quite literally get around 2000 kills with each chainsaw now before having to worry about losing it. If that doesn't sound worth it to you, I say you're nuts.
A pain to obtain, but so very worth it. You must complete the Zombie Genocider achievement in one playthrough and get an ending to have this weapon added to the security room. So you're talking one full playthrough of 72 hour mode just for this (well, maybe some other achievements too, if you feel like it). However, the Mega-Buster is available right when you start the game and holds 300 shots. I never even used all 300 in this playthrough, but I did use it for several Psychopaths and the Convicts at least 3 times. You can literally kill the Convicts from far enough away that they won't even have seen you yet with this thing. They go down with one shot apiece.
This gun is extremely powerful and will respawn infinitely even if you do use the whole thing (but you can never have more than one in your inventory). This isn't a requirement by any means, but I highly recommend taking the time to acquire it, because when you have 6 survivors in Leisure Park and the Convicts have respawned, you're going to really wish you didn't have to deal with them again.
I'm not the type of guy to carry around several Queen Bees all the time and use them to clear out paths constantly. I'm quite content with just slashing down everything in my path with my Mini-Chainsaw. However, having one Queen on hand at all times is a really good idea. Sometimes you just run too far away from your survivors and they end up in a swarm of zombies, or occasionally your survivors are trapped by a swarm of zombies when you find them, and these times call for a Queen Bee to ensure your survivors' safety.
Sure, it's no problem for you to slash away those zombies with your Chainsaw, but with your survivor standing in the middle of them, 9 out of 10 times you're going to whack them as well, and you probably don't want to do that. So just hold on to one Queen Bee as much as possible for those emergency situations.
So now that's 2 Chainsaws, 3 Books, 1 Mega-Buster, and 1 Queen Bee for a total of 7 inventory slots used. That leaves 5 more slots (if you've acquired all inventory slots) to do whatever you want with. I recommend stocking 1 of those with a Hunting Knife to give to your survivors, and the rest with Orange Juice. Really, you can use whatever type of drink/food you like the best, but I love to grab lots of Orange Juice because it's right at Columbian Roastmasters in Paradise Plaza — easy to get to and great for you. Plus, when you do accidentally take a swing at one of your survivors, you can just toss them a jug of this stuff and it will heal them right up. Just remember that when you do, they will drop their weapon and you will need to pick it up and give it back to them.