I've noticed that theorems in textbooks roughly come in two varieties: those that are worth trying to prove yourself, and those that aren't. I'm not going to try and give criteria for "worth trying" and "not worth trying" (I'm not even sure that I could) but I will give an example of each that will hopefully illustrate what I mean.
Worth trying: All Sylow p-subgroups are conjugate to each other. To go about proving this you are forced to consider a group acting on itself by conjugation and see what information you can extrapolate about the group itself from the action. Along the way you are naturally led to consider the the group acting on its subgroups and order/divisibility arguments about subgroups, both of which are useful ideas which can be applied to many other problems. Even if you aren't able to come up with the proof, your efforts will likely have led you to develop tools and consider ideas which will be helpful later on in group theory.
Not worth trying: Alternating series test. The technique used in the proof is very ad hoc and unlikely to improve your chances of proving/understanding any other results in real analysis (or even results related to series for that matter). While the proof is cool and undoubtably rewarding to discover yourself, in my opinion your time would be better spent simply skimming the proof or even just using the result as a black box.
So my question is this: how does one decide which theorems are worth trying to prove yourself? It's easy to see in hindsight once you have a "big picture" view of the subject, but when you are first learning it is much more difficult to discern which proofs contain tools and ideas which are ubiquitous in the subject, and which are worth attempting to develop yourself.