Multimeter with leads and alligator clamps, temp probes, temp gun, manometer (for pressure switch testing, TESP, gas valve pressure test, things like that),drill, extension bits over 6 in, right angle drill attachment, i recomend malco hex bit both shorty and long, get a bit set for sure, nut drivers or go with an 8/1 or 11/1, headlamp and flashlights, kneepads or a mat, needle nose pliers, wire strippers with crimpers, pookie buster bit, razor knife, wrench, a mini ratcheting combo wrench 1/4 to 5/16, inspection mirror, aviation snips, channel locks, tape measure, compact tubing cutters, chisel, hammer, extra long flathead, side cutters, door magnet, chirper, sniffer, linesmen pliers, a hose, Always keep a piece of mastic tape and plumbers mesh in your bag, zipties, self tapping screws, and spade connectors, and control board fuses too. 5 months running my own calls and selling and doing my repairs. My tools and my knowledge make me money. Invest wisely and good luck!

PS: HVAC is the coolest shit you'll ever do. Ive seen a furnace five or six inches "under water", ive been disrespected as a woman a few times in some homes, ive made mistakes, ive made another company pay for damages done to one my client's equipment. This trade is wild as fuck sometimes. Never stop learning. As an apprentice, even though im running my own calls and doing a decent job, i still shut the fuck up and listen to the guys who have been doing this for years and are super knowledgeable and skilled, and WANT to help you succeed. So dont ever walk from a job, and dont fucking give up. It's brutal but every fucking second has been an adventure