Strength training is a very important aspect of being healthy, there is a mountain of research to support strength training for:
1. Injury prevention
2. Bone density improvement
3. Performance enhancement (speed, power, strength)
4. Decreased body fat
5. Increased flexibility/mobility
Any great body needs to be a strong body. For the workouts you do, never accept them as is. Think about them critically and decide whether they make sense for you. Muscles are your movers so it important to train them because strength is the base for all movement. NEVER sacrifice form for weight or more reps. It’s okay to start small as long as you have perfect form. You CAN always add weight, you CANNOT take away an injury.
Here are exercises that you must do at least once per week:
Single leg exercises: There are several variations each of these channels, I like
the Single leg RDL http://www.youtube.com/watch?v=SVCw9HRUuow ,
the RFESS http://www.youtube.com/watch?v=oEsZz8Vccpw
and lunges http://www.youtube.com/watch?v=lhFQxwGOUmE … there are many others and you can play around with these.
For the upper body you need to each of these at least once a week: (I would probably do a vertical push/pull one day and a horizontal push/pull the next)
Horizontal Press (ie Bench or Pushups)
Horizontal Pull (ie Body Row or DB Row) http://www.youtube.com/watch?v=b9IHiL2pssw
Vertical Press (ie Military Press) http://www.youtube.com/watch?v=DTBSJ8oenXk
To be the most efficient I recommend to start with 2-3 full body workouts a week. You should be able to get through a lower body lift, upper push, upper pull and single leg exercise in 20-40 minutes. Do lots of core and core type exercises, the plank is the absolute best. But if you also want variety, the channels I gave have lots of variations you can try. After preforming your main exercises you can move on to your secondary lifts (aka curls). Make sure to warm up and cool down and you can do all this in under an hour.
Finally, I really recommend writing down everything in a journal. This way you can track the improvements that YOU WILL see. Too often I see people randomly choosing weights without tracking their progression and staying around certain ranges of weight for too long. By logging workouts you can reflect on what is working, what you can build on, and what you need to change.
I hope this helps you structure simple but effective workouts. Remember this is just a base for a plan. Every 2-6 weeks you should be changing something. If you have questions about programming principles please send them my way.