The most important factor when creating a home gym is maximizing the space you have to work with. In my opinion, a set of PowerBlock dumbbells is mandatory. https://powerblock.com/products/elite-usa-90-adjustable-dumbbells They give you the ability to grab a pair of dumbbells anywhere from 10 - 90lbs, and when you combine those with an adjustable bench, you literally have almost everything you need for a complete workout. https://powerblock.com/products/powerbench-2-adjustable-weight-bench The bench above even comes with attachments for doing dips and pullups.
Here is a novel idea: Why not both? This is the best time to get a new gym membership for the new year, and about 2-3 months from now will be the best time to buy almost brand new equipment slightly used, because people realize that they are not going to follow through their new year's resolution. Recently I tried to sell an elliptic machine on Craigslist, that was hardly used. Original price was over 3K, I couldn't find a buyer for 600. Gave it away for free. There were at least half dozen similar machines for sale, their prices were like used diamond's, 80% below original. So why don't you plan to buy maybe 2-3 machines and free weights, but also join a cheap gym? You can generally work out at home, but 1-2 times a week you go to the gym to use their super-duper special machinery? Maybe you can even make some friends. And over time you are going to see if membership motivates you, or you hate video makers and other distractions. Special warning: Gyms are going to be full of new members in the first 6 weeks of the new year. Then suddenly it will get better... "I pretty much don’t even bother going to my YMCA the first three weeks of January. It’s a madhouse. Then the Super Bowl happens and it clears out."
I find the best time is on getting up, before breakfast, eating nothing so you don't get a stitch. Then shower. So it's most practical to exercise at home. Mind you I'd just get a welder, chop saw and grinder and make my own equipment. Or using wood, can look very cool.
I second the power block, especially for uses over 40pounds. Less than that a regular dumbbell is better because the shape makes them easier to manage for those exercises (at least for me)
I do not think most people work out more if it's a home gym. There wouldn't be such a supply of deeply discounted home equipment if that were the case. The absolute key is doing a workout that you enjoy for whatever reason. That's the one you will stick with and do with intensity and joy. Staring at your concrete basement walls is typically a tough environment for all but the hardest core trainee.
nothing like.sweaty asses sitting on cloth couches and loungers.....must smell like a snake's vagina in there...
I go to a huge gym. Hundreds of machines. Two heated lap pools, one on basement and one on roof. Reasonable yearly subscription. I go everyday but only use the pool and three or 4 machines.