sleep tracking is hit or miss. ultimately it doesn't really do anything except give you info on something you can't really control cuz, you know, you're asleep. Going to bed on time and getting enough rest is key, but a tracker isn't needed to accomplish those goals.
pulse, aka heart rate, can be good to track when you do cardio exercises but I think for someone just starting out in fitness it provides quantitative measurement when you don't necessarily need it unless you're training at a higher level.
I'm not sure how you'd track stress?
Here are the things that I think you should track if you're wanting to pay more attention to your health. Track what you eat, particularly your total calories and macros breakdown (protein, carbohydrates and fats) Apps like MyFitnessPal make it easy to look up the nutritional content of foods and you can log what you eat to track your macros.
I'm a huge advocate for strength training. it is the most efficient, bang for your buck in terms of time. Starting Strength is a great program to start out with, so is Stronglifts 5x5. The caveat is that you need access to a gym with barbells. There are apps to track your workouts but I personally just use a little notebook.
Better health comes down to eat well, sleep well and build strength.
Hope that helps!