Quoting: CharlieB
I dont know about benchpressing and squats, i dont want to put any excessive strain on my back because i want to squeeze out whatever few centimeters i might have left within me!
Neither of these exercises cause spinal compression, so you shouldn't have to worry about losing any height

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What's the reasoning behind doing cardio after doing weights?
Doing weights first lets you get the most out of your weight lifting session, without being tired out from cardio. Also, you can do cardio when tired and not worry about dropping weights on yourself

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And do you think maybe focusing on pull-ups instead of weight training for my biceps and shoulders will work better?
No, don't replace for pull-ups. Pull-ups make a good addition to any program though.
Like Bionic Samm, I recommend you try out the Stronglifts program. Almost every one of the Stronglifts exercises involves back and shoulders. I don't recommend only doing exercises that *only* target specific areas, as this can lead to muscle imbalances, which in turn can lead to injuries.
If you decide not to follow the stronglifts program, do as Bean says and multiply everything by three. Do three sets of each exercises. Increase the weight whenever you can and do 8-12 reps for each set. If you can do more than 12 reps easily enough then increase the weight. If you're unable to do 8, decrease the weight.
Also, get a wider variety of exercises.
- Chest/Triceps/Abs
- Back/Biceps
- Shoulders/Traps
- Legs/Calves
You should be targeting all those areas. Cram it into 3 days if you want. Stronglifts does this. The stronglifts exercises are well-chosen to target as much muscle groups as possible.