How strong should you get through training?
All strength standards are based on relative strength. The weight you are lifting in comparison to your bodyweight.
The most popular set of strength standards is using the barbell
Barbell Standards
You could also use Dumbbells
Dumbbells have limitations. As you get stronger, the dumbbells get bigger, and harder to stabilize. Eventually it becomes more practical to use barbells or machines.
DB Reverse Lunges with 100% bodyweight for 10 reps
DB Goblet squats with 1/2 bodyweight for 25 reps
1-arm DB rows with 1/2 bodyweight for 10 reps
DB Chest Press with bodyweight (1/2 per hand) for 10 reps
DB Romanian Deadlift with bodyweight (1/2 per hand) for 20 reps
DB Shoulder Press with 1/2 bodyweight for 10 reps
You could also use bodyweight
BZP Big 4 Strength Standards
Dips
Beginner-20 reps bodyweight
Intermediate-10 reps with BW +25% of BW,
Heroic Strength-5 reps with BW+50% of BW in added weight (that would be a 200lb man with 100lbs in plates on a dip/chin belt)
Weighted Chinups
Strength goals
Beginner-12 reps bodyweight
Intermediate-10 reps with BW +25% of BW,
Heroic Strength-5 reps with BW+100lbs in added weight (that would be a 200lb man with 100lbs in plates on a dip/chin belt)
Bulgarian Split Squats
Beginner-20 reps bodyweight
Intermediate-10 reps with BW +50% of BW,
Heroic Strength-10 reps with BW+100% BW in added weight (that would be a 200lb man with 200lbs in external load)
45 Degree Hyperextensions
Beginner-20 reps bodyweight
Intermediate-20 reps with BW +50lbs
Heroic Strength-20 reps with BW+100lbs in added weight (that would be a 200lb man holding onto a 100lb DB)
What if you never come close to any of these numbers?
The reality is that genetics determine how strong you can get. You may have exceptional strength in one area (maybe you are a fantastic bench presser). You could be mediocre in another (you struggle to deadlift more than 2x bodyweight).
You dont need to have elite strength to be an elite athlete
World champion boxers, kickboxers, muay thai fighters, they dont have elite strength. Your bench press and your punching power dont correlate all that much. Having long arms and a torso that can rotate is very different from having refrigerator sized ribcage and massive joints.
How do you know if you have the genetics for ELITE strength?
if you have to ask, you dont. You would have learned this within the first 3 months of lifting, when you were naturally stronger than everyone else, and built muscle faster.
How long does it take to become ELITE?
Reaching Elite strength you can assume will take 2-5 years. Again, this depends on genetics. Also training consistency, and nutrition. The better your genetics, the faster you reach elite. The worse your genetics, the slower (or never).
Regardless, get as strong as you can, in as sustainable a manner as possible