The only valid suggestion for getting bigger without surgery is to bulk -- bulking just means to eat enough to gain weight.
Meal frequency/timing doesn't matter, so long as you consume enough energy (calories/kilojoules) to grow on a daily basis.
I don't see any benefit in gaining weight and then starting to train...or have I misunderstood you? Anyway, if you wait until you've gained 5-7kg and then start training, then you will have only made yourself 5-7kg fatter, rather than having gained useful muscle in that weight. Better off getting into training and beginning weight gain simultaneously. If sports are a motivator to train, then doing daily resistance training isn't necessary. You'll probably be best to start off with 3 non-consecutive days per week of full-body training (squats, deadlifts, bench press, overhead press, pull ups or pull downs, rows). Since you're only 14, I'd be careful to make sure that you're confident you could do at least 2 more reps at the end of every work set of each exercise, and stick to rep ranges between 8 and 15. This will protect you from injuries, especially to your bones/growth plates, while giving you sufficient stimulus to get bigger and stronger.
For how to motivate yourself, I don't know. When I was your age, slightly shorter and even lighter, consistently losing arm wrestling matches to 12 year old girls gave me sufficient motivation for life. If you genuinely want to play sports, as you say you do, or just to be able to resist getting your head flushed in the school toilets, I fail to see how that isn't motivation enough on its own. The best motivator is love: love what you're doing, or if you can't love what you're doing, at least love what you're doing it for. Fear is also a good motivator, although I'm not encouraging you to be fearful of the world, just to use it if you are afraid: afraid of not being able to participate in rugby and the like; afraid of getting beaten up by the bigger, stronger kids; etc.
