It’s an expensive investment. If you are going to use it in the long term it’s worth it, and btw a complete home gym can cost less than an high level bike. In my opinion the minimum is a barbell, the rubber plates, dumbbells, some rig/rack, a bench and a rubber floor. After that if you see that you like that you can gradually upgrade it with new tools, like kettlebells, gymnastics rings and whatever you want.
I did it and I really like it. I’d avoid rigs, racks and benches from Amazon because usually those aren’t good, but like someone else suggested to you, you can find very good used stuff, that’s like new. I bought a lot of rubber plates that were used but really like new, I’m talking about competition rubber plates that I’ve paid about 4-5 € /Kg. Today I’ve bought other rubber plates, not for competition but very good ones at 3 € /kg; used but like new. If you’re patient you can save a lot of money in this way.
The fact that you have your own gym doesn’t exclude that from time to time you can go in a gym, it’s always good to have the opportunity to receive feedbacks from professional coaches.
So in point of view, the pros are:
Time saving
Availability of tools
You can focus better on exercises
Cons:
Social aspect
No feedbacks from coaches or other people ( I suggest to film yourself while doing exercises)