Squat rack vs Smith machine for home gym

In the squat and bench movement the bar travels in an arc, not a straight line. Smith machine is not a natural movement. Smith machine is ostensibly safer but with safety arms/straps on the squat rack it's a nonissue.

Plus you can curl in the squat rack

Smith machine is for chicks posting workouts on social media

I'm a huge fan of the smith machine. I believe Cybex makes the best one - it seems to offer smaller intervals for setting the stops / safety bumps. Unless you are going to squat / bench over 400lbs all day every day, the Cybex smith machine is excellent, IMO.

Lot you can do with a smith machine. Various presses, front squats, standing calf raise, shrugs. With an adjustable bench you have a ton of options. That said, the main reason I started using a smith machine is because for many, many years I could not find a reliable workout partner and I opted to use a smith machine so I could keep my music on full blast, not have to talk to anyone, and didn't have to worry about a spot if I wanted to lift heavy. Also, with some injury issues it gave me more flexibility on ROM. For other stuff where I wanted to attend to balance, proprioception etc, there were dumbells, lunges, and so forth. As much use as I've tried to make of a smith machine, and as much as I like them, I still make use of the racks as well and there are plenty of things a smith machine is simply not suited for.

Back when I started making use of a smith machine, the options on power racks were not out there. These days, with the chains, belts, straps, rods, etc etc etc you can get for a power rack, from a good manufacturer like Rogue - If I was building a home gym and had to choose between the two, it's a power rack. There's almost nothing you can't do in a power rack.

Why not both? If it's space, get the power rack. If it's budget, then a power rack with quality barbells / dumbells / benches to go with it would be preferable. If your budget and space allows, I would seek to have both. If not, the power rack is the way to go, most likely.

Another consideration to think about with regard to price and budget is the barbell selection. If you can lift good weight, get proper bars for the lifts you plan to do. If you are lifting really light weight, then it doesn't matter until you advance a bit more. If you can lift considerable amounts, it matters. For example, a deadlift bar is really good for deadlifts, but if you were to do standing barbell behind the back wrist curls, it probably wouldn't work that well. The way the bar and collars mate together and rotate, along with whip, will affect things. A good barbell matters. Power rack with a proper assortment of barbells is really good to have. If you're serious about lifting, being able to grab the right barbell will be appreciated every day. It is a worthwhile expense.

If there's a good gym in your area, particularly if it's open 24hrs, so you can go whenever you want, that is far cheaper. If you really need a home gym, I wouldn't go cheap and I'd build it out as well as you can. People I've seen that go cheap end up not using it. Equipment breaks, not as comfortable or versatile, doesn't seem as stable, and so on, and they stop using it and it's wasted money.

I have ranted long enough.

Good luck.