As far as gaining muscle mass goes, both lighter weights for higher reps and heavier weights for lower reps will work. In common thinking there are 3 types of muscle fibre: slow twitch, fast twitch A, and fast twitch B. In reality, there are several more muscle fibre types than these 3 categories. Each type of muscle fibre is activated best at a particular intensity (%1RM) and after a certain period of time has taken place, fatiguing the previous muscle fibre types. Consequently, you can get good growth doing heavy singles, and you can get good growth doing sets of 20, and you can get good growth at different rep ranges and volumes (volume = reps x sets) in between. The main thing is to focus on progressive overload (consistent increases in workload by increasing either the weight or the volume) on a balanced routine, with plenty of food for growth.
As far as specifically increasing your maxes goes, you generally want to stick within 1-10 reps per set. More reps per set beyond that point does relatively little to increase your 1RM, just as how increasing your 1RM does very little to increase your 20RM, because of the different stressors and adaptations required. The ideal rep scheme, for the most part, is 3x5 (3 sets of 5 reps) on most exercises (some will need different schemes, such as olympic weightlifting exercises needing less reps but more sets, due to the technicality of the lifts; and deadlifts often progressing just fine with a single heavy set after properly warming up for it), and for a beginner, a program such as Starting Strength by Mark Rippetoe which takes advantage of this rep scheme is a very good place to go. You are a beginner, so I recommend starting there.
3x5 is good because it allows you to get close to your 1RM, often creeping to within 80-85% of 1RM. Lower rep, higher intensity sets, eg 3x3x90% 1RM, 3x2x90-95% 1RM, are more specific to increeasing your 1RM, so you'd think they'd be better for improving maxes, but they're also very neurologically taxing, so you burn out quite easily at that intensity. Higher rep, lower intensity sets, eg 3x10x70% 1RM are so far removed from the load of a 1RM that while movement patterns are the same, technique will be different, so they don't have a very direct carry-over into 1RM progression.
As you become more advanced, your training requirements will change. 3x5 will still be a good sweet spot to a large extent, but your workload will be much higher than as a beginner, and fatigue will creep in more rapidly. One option is to vary the volume and intensity throughout the week. Another option is to periodise training, by spending some time doing sets of 10, then progressing up to sets of 8, then sets of 5, then testing 1RM. You might do that over 3 months, eg 2 weeks of 2x10, 3 weeks of 3x8, 3 weeks of 3x6, 3 weeks of 3x5, test 1RM. You don't need to worry about any of this now, I'm just writing about it to let you know how different rep ranges benefit max strength training.
I don't know when your school year ends, but if you focus on good technique and small but frequent progressions, you could probably put 25-50lb onto bench press over the next year, and 50-100lb onto deadlift in the same time. Of course, that's very individualistic. Some lifts you'll be better built for than others, and they'll progress easier than others. Some lifts will psyche you out, and you'll struggle to progress because of what's going on in your head, not because of your muscles lacking the required strength. Some lifts you'll be more excited about than others, and you'll be more able to push yourself through tham than others. For example, when I'm training heavy in the 5 rep range, it feels like doing a 3RM, and then 2 more impossible reps, because I'm able to push through it, whereas on bench press, once I've hit what feels like a limit the set has to end, because the bar won't come up again.
