You will achieve this absolutely critical stability by following a workout program where you are:
1) Focusing on getting stronger. This should be your main focus as a weak body is an unstable one, and will prevent you from achieving your goals AND staying healthy.
2) Training all of the basic movement patterns that you will be required to perform in your daily life, workouts, or sport. This includes squatting, hip hinging, lunging, pressing (vertically and horizontally), pulling (vertically and horizontally), and loaded carries.
3) Selecting appropriate exercises for each of these key movement patterns. They should meet your current fitness level and capabilities.
4) Lifting as much weight as you can for your desired rep range but while using good form at all times. Check your ego at the door and make sure that you are using good form 100% of the time.
5) Working on mobility in areas where it is lacking.
This is what will give you the stability and solid base so you will be able to achieve your goals, AND stay healthy. You would never build a house on a weak and uneven foundation, and the same principle should apply to your body. Now it's time for you to get strong and stable, and to achieve all of your goals!