This is just about getting started with strength training. For those who have little or no experience with the topic.
First of all: Strength training is exercises hard enough that you can only do 12 in a row or fewer. Or, with isometric exercises, something you can only hold for less than 30 seconds.
Otherwise what you are doing is endurance training. Which is not the same thing.
Primarily, it's not about which exercises you do, it's about the intensity at which you do them. Bodyweight squats are an endurance activity for most folks because they can do 15 or 20 or more. But if you did the exact same exercise while holding weights - enough weight that you could not do more than 12 - then the exercise would be strength training instead.
If I were to recommend a set of dumbbell exercises (since adjustable dumbbells are cheap, readily available and useable at home) I'd suggest the following:
1. Squats
2. Split squats
3. Straight leg deadlifts
4. Hip thrust/bridge with weight (you can start this with dumbbells in your lap. You need to put your back up against something sturdy. I push a chair up against the wall).
5. Bench press (can be done on the floor, a bench isn't necessary)
6. Bent-over row
7. Shoulder/overhead press (do this standing not seated)
8. Pull-ups (a pull-up bar can be gotten that works in almost any apartment and doesn't require tools to install). Here's a primer on doing pull-ups if you can't yet.
9. Crunches with weight (I prefer to hold the weight by my shoulders)
10. Side bends
This set of ten covers every major muscle group in the body and works them in all the major planes of motion. So it is very nearly complete.
The amount of weight you are looking for is something that will develop strength, which means higher weights and lower reps.
Start at 12-15 RM - Repetition Maximum - the number that you can do before you cannot do another with good form.
Start easy on the exercises to develop your form. In the long run good form is much more important that increasing weight quickly.
For each week pick an intensity level. Do all of your exercises at that level. Every 2-4 weeks you can increase the intensity level.
Do the workout at least twice a week and each session has a rest day in-between another session. So not more than three times per week.
Aim for multiple sets of each exercise. 2-3 sets is a reasonable workout.
But if you only have time to do one of each then start there.
You need to rest between each set to get the most out of it.
12-15RM - rest 60+ sec.
8-12RM - rest 90+ sec.
7 RM and heavier - rest 2-4 minutes
You can shorten the rest periods if you alternate exercises between different muscle groups e.g. push/pull or upper/lower. But you'll still need rest between sets. This sort of plan can be done on "light" days.
For strength training you should also have a "heavy" day where you don't alternate like this and you take appropriate rest periods.
Start easy on the exercises to develop your form. In the long run good form is much more important that increasing weight quickly.
For each week pick an intensity level. Do all of your exercises at that level. Every 2-4 weeks you can increase the intensity level.
Intensity levels:
12-15 RM
10-12 RM
8-10 RM
6-8 RM
12-15 RM
10-12 RM
8-10 RM
6-8 RM
I wouldn't go higher than that without a spotter though.
Do the workout at least twice a week and each session has a rest day in-between another session. So not more than three times per week.
Aim for multiple sets of each exercise. 2-3 sets is a reasonable workout.
But if you only have time to do one of each then start there.
You need to rest between each set to get the most out of it.
12-15RM - rest 60+ sec.
8-12RM - rest 90+ sec.
7 RM and heavier - rest 2-4 minutes
You can shorten the rest periods if you alternate exercises between different muscle groups e.g. push/pull or upper/lower. But you'll still need rest between sets. This sort of plan can be done on "light" days.
For strength training you should also have a "heavy" day where you don't alternate like this and you take appropriate rest periods.