Congrats on your resolve- I assume this is a new year's resolution? Hope it lasts.
If you want to get stronger, you will need to focus on what are called compound exercises.
These are the squat, the deadlift, the bench press, the shoulder press, the chin-up, etc. They are ideal in improving core strength, but are difficult to master and you will need to practice them a lot. Try looking for a personal trainer.
3x a week training is ideal. Try making these full body workouts, which means 2-3 of the above exercises (don't do deadlift and squat on same day, it's too much for your CNS), maybe a couple of isolation exercises (triceps, calves) and an assistance one (abs).
You're very skinny for your height... you need to start eating and also learn about nutrition.
This website:
http://www.bodyrecomposition.com/ is the ultimate reference for nutrition and also included quite a bit of training.
Finally, it's consistency that will be your main hurdle... if you're serious about this, you have a lot to learn and will often need to be ready to change things as you learn more...