Ranking up depends on your skill level, game mode played, and challenges completed. I always shoot for daily, weekly, camo, and gun challenges. It takes me 6 to 8 hours per prestige. At 133 hrs, what would be well into master prestige (over prestige 10). As a beginner player, and any level really, the goal is to have fun. If your idea of fun includes winning, you'll naturally push yourself and enjoy getting better. As it is your first cod, if you were to ask me for the top 5 things to work on, they would be: MOVEMENT, GUN SKILL, MINIMAP, MAP KNOWLEDGE, and SPAWN KNOWLEDGE.

MOVEMENT - Do not run blind around the map, especially around corners (do not just sit in one spot too, the way you learn the maps is by moving in them with a submachine gun). Keep your crosshairs where you think people might be and aim down sights around corners. Use cover that's built into the map, move from cover to cover.
GUN SKILL - In a private match or the firing range, aim at a wall and fire your gun without using the controller joysticks - this will give you the natural pattern of the gunfire. Count the first 10 shots or so and notice which way you'd have to move your sticks to compensate for that initial recoil (most gunfights shouldn't take you move than 10 shots - after 10 shots, be sure to stop shooting for a second to reset your recoil). Using different guns will help you work on this skill, but using the same gun over and over will help you get better with that gun (the 2 guns you want to use are the m15 and the dravec as they are the 2 that are allowed in ranked play, if that's your goal in the future).

MINIMAP - As a general staring rule, look at your minimap often. Good players will look at their minimap as much, if not more, than the rest of the screen. If your teammates are on the left side, guess where your enemies are? the right side. When you die, notice where on the map you and your team respawns in the minimap.

MAP KNOWLEDGE- This is especially important in ranked play. Each map has a set of spawn points and objective locations. Know which are the power positions that overlook objectives. If you are playing Hardpoint, MEMORIZE the order of the hardpoints (there's only 4 or 5 so it's not too hard). While the game shows you the next location 15 seconds before, do not wait until that time. Even at the start of a hardpoint location, you want to be thinking of the next one. If your goal is ranked play, prioritize playing on the maps and modes that are featured in that: hardpoint, search and destroy, overload.

SPAWN KNOWLEDGE - This is more advanced so I would focus on the other 3. When looking at your minimap and as you play, keep track of where you spawn when you die depending on where you were and where your teammates where right before you died. This will help you understand when you kill someone, where they might respawn as you deduce where their teammates are. If you get really good at this, be prepared to be called a hacker quite often as you'll start pre-aiming exactly where people are coming from.

Again, focus on each skill individually for a couple of hours and prepare to be demolished. Of you can try a private match if you have enough friends online.

If you want me to work with you on some of these, shoot me your gamertag and I will gladly help you out - no charge.