Jeep: unparalleled utility. It'll die eventually, fuel is finite, but it'll let me establish.

Shotgun: need a weapon, and while not the strategically beat weapon, I have an image to maintain.

Water purifier: water.

Machete: backup weapon, infinitely useful tool, more rugged than the katana.

I think this combination gives me a good shot at establishing a base of operations, securing the area, and settling for long-term. Between the jeep and the machete, most obstacles can be overcome, and scavenging is easier and quicker. Strategically, the crossbow is probably the best weapon just due to the reusability of the ammunition, but it's not infinite and what you gain in that, you lose in ease of use, which is paramount in a stressful situation. Opting purely for usefulness, the pistol (assuming subsonic rounds and as quiet as possible) probably offers the best balance between reliability and forgivingness, but I like shotguns.

Water purifier is a pretty easy one. Gotta have water, and while most of that will come from rain or scavenging, there will inevitably be periods of literal draught. Finally, the machete. A knife, a backup weapon, a crowbar. Good for clearing small-medium vegetation. Honestly, the uses are limitless, perhaps second only to the jeep.

Honorable mentions:

Dog. If it's pre-trained, top tier. If you have to train it, mid at best plus another mouth to feed.

Any other firearm: mostly preference, each has pros and cons

Body armor: depending on the zombies, top tier (walking dead style, feral gonna bite you zombies) or reeeally not useful (anything spread by spores, fumes, fluids, etc.)

Gas mask: invert the body armor.

Motorcycle: quicker, less utility than Jeep. I wouldn't say it's the worst pick

Everything else is either marginal utility at best (cb radio, NV goggles) or easy enough to scavenge (flashlight, first aid supplies, tent, honestly everything else on the list.)