You must really take into account that drag is terribly calculated in this game, for your benefit. Bad as in,
this is my most effective rocket. Overengineer everything as best as you can. Dump all aerodynamic parts, they're just dead weight. Dump the winglets too, they're sort of a little useful for the first 7 km, after that they're dead weight. Your rocket's engines have thrust vectoring, meaning they can slightly aim their nozzle in a direction to steer. The best idea for you is to install
kerbal engineer redux. It doesn't fly your rocket for you, or give you tips, but it gives you a delta-V measurement for your ship, which is basically a measurement for how many meters/second you can change your velocity with your current setup. More = good. Getting into orbit takes around 5000m/s dV (that is with a large marigin included). The main reason you should use this mod is that it tells you if your modifications to the rocket are making it better or worse. More boosters is not always good, for example if they weigh so much the rocket's acceleration gets down to such a low amount you spend way too much fuel even getting off the ground.
Also, great tip if I may say so myself: Kerbin has biomes. Each biome has it's own science. So for example, doing science above the ocean is different than above the desert. You might have known this. What you might not have known, is that it's really efficient to just make rocket 'hops' that get you halfway into space, but you land somewhere on Kerbin. Now, once you are landed, do science. All of it. Crew report, EVA report, science bay, goo canister, but most important of all, take a ground sample. Then hop into your rocket, and recover the vessel. This will give you a science boost. Funny how so many people start exploring the moon before they explore kerbin itself. Also, do note that there's 4 levels of altitute to get science at: ground, just above the ground (like literally 10 meters), space low above and space high above. I think for kerbin high space starts at 250 km height. So for each biome you can get 4 types of science.
EDIT: Just read the above posts. If you install kerbal engineer, if you want a successful rocket, make sure it has a delta V of at least 4700 m/s and a TWR of at least 1.25. If you're going to the moon take at least 6600 m/s dV with you. If you want to come back too, count on 7500 m/s.
P.S. If you launch a rocket, always always always launch EAST. This adds Kerbin's rotational speed to your orbital velocity, so you effectively need less fuel.
Source: I did my thesis on this game and recieved 82.3%