I bought dumbells about a year ago and this allows me to do weights at home. As someone who has been attending a gym for many years and still do many days a week, I can honestly say that the difference being able to do weights at home has made is huge. For example, I did a session last night before going to bed, can do so in the mornings or listening to the radio if I wish. I've done a lot of sessions that would not have happened at all if I had to wait until I had time to go to the gym so my performance in the gym when I go is far better. It also means that I can spontaneously do a session whenI'm feeling energetic. Many times when I get to go to the gym it'll be after work or whatever and I'll be relatively tired so having weights at home gets around that.
Just for some context, I would never have been someone who went to the gym with another person or in a group. I'd always work out alone anyway so this involves no change but I found it to be far more effective. (I see people in pairs at gyms and the seem to waste an awful lot of time - as in hvaea lot of downtime watching each other.) At the end of the day motivation is crucial. People buy weight/equipment and it gathers dust in the home not because the weight/equipment is a bad idea, just that the motivation is not there in the person. I'd have my doubts if anyone who could not motivate themselves to use weights at home would be a star performer in the gym either to be honest.
I would exclude treadmills from all of the above. I'd need to be in a gym to find the motivation to stay on one as I find it incredibly boring though interval training is not bad.