There are many many benefits to meditation. But I before I give more detail, please remember this: You only reap the benefits if you remain committed and consistent.
I have been practicing meditation now for 4 years. There are different versions of meditation, however I practice Mindfulness Meditation and Transcendental Meditation.
One of the first benefits you should experience very quickly is calmness. Within a few minutes of beginning you can feel calm wash over you, Meditation promotes the manufacture of serotonin, a chemical that effects our moods and behavior. Low levels are associated with depression and similar mental health issues. Also, as a result of this, cortisol, a stress hormone, drops to a healthier level.
Physically, with help from controlled and focused breathing reduces the work rate of the heart, blood circulation increases, high blood pressure drops. More oxygen gets delivered to the brain and muscles. After meditation you will feel reinvigorated and energetic. Over time, and not too long, this extra vitality can be felt all day long.
For best results I recommend a minimum 10 minutes every day. That would be preferable to 20 minutes 3 times a week. With practice you will notice other benefits. Much improved concentration levels, more ability to focus. Dealing with stress as and when it arises in your life can be dealt with, with much more ease. Creativity and productivity increases greatly. Better decision making, sharpened wits. Even opportunities become easier to spot. You learn that you control your emotions, they do not control you. Meditation is worth practicing for that alone in my opinion.
Emotional and spiritual benefits are on another level. There is a great ocean of consciousness in the Universe and meditation allows us to tap into this. I don't want to go into too much detail, I'll provide you with a resource, but basically meditation allows us to manifest our goals and dreams. Start small and work your way up. That is what has happened to me. You use your five senses to fully experience what it is you desire, and you send those good vibes into the ether.
The best benefit of all perhaps is that its safe and totally affordable. The only investment you really need to give is your time.