There are two ways you can use the weights, you can create a metabolic routine which will last about 20-30 minutes where you use the same weight for all the exercises and do a circuit so say 10 reps, of each exercise and then repeat the circuit 5 times of something with a one minute rest in between circuits. This is like a cardio workout. To do more of a strength based workout then you will need to change the weight that you use for each exercise as they will differ vastly. Start of by doing two sets of 15 reps with a minute rest in between sets. Do this routine for a fortnight then change to 2 sets of 12 reps, so you will need to use heavier weights now you are doing fewer reps. After another two weeks change to 3 sets of 10 reps, again adjusting the weight accordingly.
Out of that list I wouldn't bother with bicep curls of tricep pressdowns. These are isolation moves which will not burn many calories and you can work these muscles more effectively in other full body movements. Push ups for example are great for your triceps, do them at an incline with your hands on your stairs if you cannot do full length ones yet. Drop down a step when you can do a full set. Unless you have a cable machine or a pull up bar it is hard to find a good bicep move so maybe do bicep curls with a lunge, that way you are not standing still for any amount of time.
Don't do crunches as you are at risk of injuring your spine, try holding a plank for 30 seconds instead.
I doubt if you have a cable machine at home but if you have access to one then lat pulldowns and seated row are great back exercises.
So for a strength workout you could do for example, do 2 sets of 15 reps of each of the following:
squat
deadlift: these are hard to do effectively without a barbell. Single leg deadlifts with dumbbells are a great substitute.
push ups
bent over row
plank
Or
Bulgarian split squat
Step ups
shoulder military press
dumbbell pullover
reverse jacknife on swiss ball
For each exercise you would need to choose a weight that allows you to just barely be able to complete the number of reps you are aiming to do.
If you were going for a cardio type circuit then you could try holding lightish dumbbells and doing:
10 squats
10 pushups
10 reverse lunges (each leg)
10 bentover row
30 second plank
Rest 60 seconds, repeat 5 or so times.
You need to leave at least 48 hours between strength training sessions as this is when your muscles recover and rebuild. You can do cardio straight after your strength training of you can do it on your off days in between, up to you.
Concentrate on getting the form right in each exercise, eg when you squat your hip crease should be below your knee crease, you will know when you are low enough as you will suddenly feel your glutes and hamstrings doing some of the work, not just your quads. Lunges make sure you are getting enough depth, ie knee barely brushing the floor. You can make these harder by elevating your front or rear foot to give a greater range of motion. You tube is great for looking up different exercises and seeing how they should be done. Once your form is great then start increasing the weight that you can maintain that form with.
Sorry, that is all rather garbled, the book I recommended can explain it far more clearly and has great illustrations of the movements and suggestions on how to progress from easier to harder variations. It also suggests different cardio finishers you can try after a workout. For example, the leg matrix: 24 squats, 12 lunges on each leg, 24 jumping lunges, 24 jumping squats. Rest for twice the length of time it takes you to do and then repeat. It hurts...a lot 