Assuming I don't have to purchase the clothes I wear every day (hiking boots, jeans, flannel shirt, hoodie, and leather jacket) this would be my list:
Used mountain bike with spare chain, spare tire, small hand-pump, etc = $200
Used single-shot 12 gauge = $100
Set of chamber adapters that let me shoot .22, 9mm, and .357magnum out of the shotgun = ~ $75
325 rounds of .22 = $25
100 rounds of 00-buckshot = $50
25 rounds #6 birdshot = $7
20 rounds 12 gauge shotgun slugs = $13
Small bottle of gun oil = $5
Decent quality machete + sheath = $50
Decent quality fixed 6" blade knife + sheath = $75
Decent quality folding knife + sheath = $35
10 ferrocerium fire-striker rods (scrape with knife to produce sparks and light fires) = $15
Three small tarps (8x10ft) = $50
200 ft of paracord + 100 ft 3/8" thick rope =$50
Sturdy backpack = $50
Smaller day bag, like a waist-pack = $25
4 bars of soap = $10
Tinted safety glasses = $15
3 el-cheapo LED flashlights = $25
50-pack of batteries for the flashlights = $25
As much duct-tape as $15 will buy = $15
As much shoe-goo (super-strong rubberized glue meant for shoe repairs) as $10 will buy = $10
$15 cheapo first-aid kit, plus however much rubbing alcohol $105 gets you = $25
At that point, I'm looking at $900 of stuff, which would be about $1000 after sales-tax or shipping. Assuming I could source this stuff locally and I lived in Oregon where there is no sales tax, with the remaining $100 I'd get:
Two lifestraw water filters = $40
Two bottles of iodine tablets = $10
Used .22 bolt-action rifle and a hacksaw blade, with the intention to cut it down post-appocalyse into a makeshift pistol (don't do this while the world is normal, this is illegal in most places unless you jump through some significant legal hoops/paperwork/additional taxes) = $50
This would give me in total: mobility to easily travel over 50 miles per day, in a quiet and relatively easily repairable vehicle (bicycle), which is better long term than a motor vehicle. I'd have shelter and the ability to collect rain-water (tarps+paracord) and 2000 liters worth of water purification (lifestraws+iodine). I'd have a little over 500 rounds of ammunition at a weight of roughly 15 lbs (yet another reason the bike is helpful), a shotgun that can also use the two most common pistol ammunition types that I might be able to scavenge and can also share ammo with my makeshift pistol. Additionally plus, a .22 fired in a shotgun barrel with the adapter ends up being relatively quiet, not hearing-safe, but quiet enough to not damage your hearing as much as a 12 gauge, nor attract walkers from as far away, because the barrel is over-sized and acts almost like a crude suppressor. While granted it's not the best gun out there, it freed me up to get more supplies and can likely be replaced with something better at some point, and can be repaired more easily than most other guns if I don't replace it. I have enough duct-tape and glue to make minor repairs to tarps, bags, clothes, equipment, and can also make light armor to protect against bites on my forearms and legs, and if I really needed to the tape/glue could be used to close wounds that normally would require stitches. My first aid kit is a bit lacking, but has at least the bare necessities and could keep me in okay shape until I could get better medical supplies. The fire-starting rods are important to me because while I'm sure I could find lighters and matches early into things, those break/are lost more easily, and don't tend to work as well in wet or very windy conditions. The machete makes a good melee weapon and utility tool, and the other knives are just there as backups for it. The soap is important because frankly I want all the zombie guts to come off me at the end of the day, and soap is also just good for maintaining good health. I considered adding in toothbrush and toothpaste here (with no guarantee that you'll find any surviving dentists, an infected tooth could actually be life threatening) but I assume looters for the most part will leave them alone, and even if they don't you can make chew-sticks and brush with sand or clay (gross as it may sound) to at least maintain some modicum of oral health.
You may notice I left off clothes, food, and water storage. My thought process on this is as such: cookware is one of the least likely things to get looted, and can be pretty easily sourced as needed. The clothes I wear day to day are sufficient for temperatures between 45 F and 80 F, and I live in the Seattle area so I'm rarely going to find temperatures below 25 F nor above 100 F unless I go far afield, and those very cold and hot periods usually only last about a week or so at the height of winter and summer. It may seem foolhardy to not pack any food, but frankly unless you plan to shelter in place food gets much to heavy to keep very much of, even in relatively small amounts. With the bike (especially if I sacrifice one tarp or find a duffle bag and convert to saddle-bags for the bike) I could perhaps carry 50 pounds of food if I really wanted to, but that's really only a few weeks worth at most. This setup is primarily to get me through the first few months (during which looting for food will be the easiest, and living people will be the least violent towards each other) so I can get with a group of people I can trust, supply us with tools and more long-term weapons (given the right tools I have the machining experience to make crude muzzle-loading/black-powder muskets, and of course they aren't impossible to find, as I bet they would be pretty much the only thing most of the looted gun stores might have left), and fortify enough land to start into farming, probably with potatoes and beans since these are the lowest maintenance crops a person can work with, and would keep us fed until we learned/found enough books on farming to the point that we could get more creative. Obviously there's not much hunting available in my area, so that's not a reliable food source, but there are shit-tons of invasive blackberry plants, and while they will give you the runs you could basically eat (And possibly store for winter) a ridiculous amount of them during the spring and summer. I'm also an eagle scout and have a fair amount of knowledge of what local plants are edible, so if farming for some reason isn't an option, I don't think I'll stay well fed but I imagine I can at least keep from starving to death.
TLDR: bike, guns, ammo, melee weapon, tarps for shelter, stuff to fix my stuff, stuff to fix me, stuff to make my water drinkable, stuff to make fire.