What are your must haves for your home gym?
I'm lucky enough to work at a gym and get a free membership, but I prefer to workout at home these days. I like to workout first thing in the morning and it saves me time and I get more sleep (AND I NEED SLEEP) if I workout at home.
I've been working out for more than half my life, so I have accumulated a decent amount of equipment over the years. Some of it I have bought outright - a barbell, a squat rack and Kettlebells, but much of it I have gotten from craigslist, Facebook marketplace, closing gyms, and even older equipment that gyms were no longer using.
If you are thinking of working out from home you can certainly always use your own bodyweight and do not necessarily need equipment. If this is the route you wish to take, I would recommend a pull-up bar of some sort. You can use it for pull-ups (yes assisted ones too), dead hangs, knee and leg raises and you can attach resistance bands to it for a whole host of other exercises.
My pull-up bar is the one piece of equipment I couldn't live without. I have a squat rack with a pull-up bar attached, but there are dozens of variations of pull-up bars that you can choose from that will fit in your unique living space.
Amazon.com : pull up bar
You CAN simply use your own bodyweight for things like pull-ups, push-ups, handstand push-ups, walking lunges, curtsy lunges, pistols, wall sits, single leg deadlifts, bulgarian split squats, cossack squats, v-ups, planks, etc, etc,
At some point you may feel the need to add resistance, but perhaps you do not have the money or the space. Resistance bands are a great addition to any home gym. I use mine for everything: bicep curls, triceps pressdowns, lateral and front raises, band pull aparts, face pulls, chest presses, good mornings, pallof presses, banded glute walks, hip thrusts, and glute bridges to name just a few exercises.
Amazon.com: VEICK Resistance Bands, Pull Up Assistance Bands, Workout Exercise Bands, Long Resistance Bands Set for Men and Women, Elastic Bands for Stretch, Power Weighted Gyms at Home Fitness Equipment : Sports & Outdoors
You could also add a suspension trainer as they do not take up very much space and again add a whole host of other exercises you can do. I love them for hamstrings curls, assisted pistols, chest flies, inverted rows, plank to pike, and more. You can buy them for under $100 on places like Amazon and Overstock, or look around FB Marketplace for used ones.
My next piece of equipment I can't live without would be Kettlebells. 3 of them - one heavy, one medium and one light bell. I find them more versatile than dumbbells and barbells, but that's a matter of preference. They're also reasonable priced and take up little space for you home gym. I love exercises such as the Turkish Get up, the Windmill, Halos, Swings, Farmer Walks, Reverse Grip Rows, all using a Kettlebell.
Kettlebells can be bought a dozens of places, Amazon, Target, Walmart, and the like, or used ones can be purchased from Marketplace, but they can often be overpriced these days. You're better off getting new ones at the same price.
Of course invest in a good mat - a NON-slip one, a not a $10 one at Marshalls that will send you slipping and sliding all over the place. Honestly, mats can be expensive AF, and there's no need to have to go that route, so be sure to check the reviews on your purchase. I find the reviews to be quite telling. And I would not recommend a used mat. A mat where someone else's feet have been all over it? Yikes. No thanks.
A bench might be something you want to invest in as well. You can use a box as a bench, or use a coffee table, or you can do floor presses if you are limited on equipment and space. I have a bench that I use for pressing, seated good mornings, rows, decline sit ups, and step ups. A good option to have, but not necessary. Again, you can use what you have around the house to make do for any of the forementioned exercises. A little creativity can go a long way.