I believe that way too many are approaching their training in the complete wrong way. They are on a specific program or are operating under a specific workout paradigm that keeps them from keeping an open mind. Staying focused with your training is an absolute must if you are looking to make the huge changes that will impact your life forever. However, being closed minded will keep you from expressing your true potential in the gym.
A very flawed approach to fitness is one that does not holistically build you as a person. There is a reason why college has a multitude of different classes. It is so that you can grow as person in multiple different areas of intellectual pursuit. It allows you to add breadth to your experiences and gain a better understanding of the life around you. The same principle applies for your training as well.
You need to focus not on just strength, or size, or speed, or aesthetics. You need to take it to the next level and start thinking about how you can perform your workouts in such a way that you touch on every single area. The main reason that I seriously injured myself and had to stall my training for over a year was because I took too narrow of an approach to my training.
Focusing on just one area is a great idea if you have already developed enough of an overall base to begin finding your area of specialization. For example, if you have already been training with high variety for a few years and make the decision that you want to get involved in powerlifting, you should go for it. This is because you have already exposed yourself to a diverse mix of exercises and training philosophies.
However, I have competed at the national level for powerlifting and can tell you definitely that the very best guys on my team where the ones who also spent time performing athletic movements as opposed to just the big three (squat, bench, and deadlift). They would do sprints, Olympic lifting, band work, and lots of core. They were concerned with becoming better all around. However, making this conscious decision to work on everything actually funneled itself very effectively into their powerlifting. The speed work helped to develop power out of the bottom of their squats. The band work helped to improve the activation of their traps during deadlifts. The core work and tertiary hypertrophy movements filled in the grey areas where small improvements could be used to capitalize on large strength improvements.
My advice to you if you are just getting started is to start approaching your training from all angles. Go in and focus on building strength with the main compound movements. However, also go into the gym on some days and focus on cardio or play a game of basketball to improve athleticism. In the long run, you will get injured much much less and just enjoy the process more. You will make vast improvements in your physique and body in short amount of time. You will look back and thank me in two years when your body is completely healthy, agile, fast, and strong.