Providing you are eating properly, I do not think you should worry too much about gaining weight as you will likely add that naturally over the next few years. If you are not gaining at all, or what you are gaining is not lean muscle, the amount of protein you consume on a daily basis could be holding your back. Recommendations vary, but a common recommended amount for an active male is to consume 1.2–1.4 grams of protein per kg of lean muscle mass to 'maintain' your weight. Adding more protein, again providing you remain active, will add to your muscle mass. Higher protein levels with low activity will create fat. Be sure to cut out as many bad calories as you can as well. If you decide to take a protein supplement as a means to up your protein, try to stick with a high quality 'whey protein isolate' as it is the easiest to digest/absorb. Consume it right after you workout/ride.
Cardio, core, and leg strength are very important for riding. For someone that is not fit, cardio comes before strength training. You are young enough that you should be doing both. A big chest, arms, and shoulders tend to cause people to ride tight, so don't try to 'get big.' If you have not already done so, take up road or mountain biking as your primary endurance exercise as it will condition your arms, legs, shoulders, and back at the same time. Strength training should be high count, fast reps, primarily with bands or non-traditional weights (medicine balls, kettle weights) instead of benching - not to say you should not use traditional weights at all, but they are less important. Routines that incorporate body balls, medicine balls, bands and kettle weights can be found online. You can also find training routines that pros use.
However you decide to proceed, be sure to give your body sufficient time to recover. Keep your 'all-out' workout/riding sessions to 1-2 per week, with no more than 2 days in a row of vigorous training before you take it down a notch or two. While building your endurance, be sure to not rest for more than 3 days in a row, with 2 being a good target. Once you are feeling good you should be able to train for 5 days a week.
Good luck, and keep in mind this stuff does not turn around overnight.