If your goal is general strength, then don't think about individual muscles. Think about movements that involve many muscles.
these are the movements:
knee dominant (squat)
hip dominant (deadlift)
horizontal press (bench press)
vertical press (overhead press)
horizontal pull (row)
vertical pull (pull ups)
a thread of vertical vs. horizontal pull is going on right now. do compound exercises for every movement to get stronger at every movement you make.
So you're saying to get strong you have to master movements first, and when you get them applying weights is just going to make you stronger with building some muscles also. Here
also says that bodyweight exercises are integral when doin that kind of workout. Is that right?
No. I'm saying that these are the movements that you need to train with weights. Like Stu says, any kind of weights can be used for that. You said that your goal isn't to be a body builder, then you talk about training the way that body builders do. I suspect that you have read some articles that are targeted at body builders, or have gotten training advice from one. I'm not saying that it's bad to be a body builder (we all love you Bob), but that they have a particular way that they train, and that you probably need to do things differently. You only need to work individual muscles in isolation if you are trying to get them to stand out from the other nearby muscles. To be strong, teach many muscles to work together.
Think about it. In daily life you don't think, "OK, I'm going to contract my biceps now." No, you just pick up whatever you need to pick up, using your biceps, your grip muscles, the muscles of your chest, back and shoulders along with the biceps. So do weight training exercises that make all of those muscles work together.