The original poster was asking about wattage and resistance. All of the information above is correct and important for safety, but doesn't address the issue of why you would pick a particular wattage in the first place. Let me break that part down.
First, wattage (W) is equal to voltage (V) times current (A). For example, if you draw 4V at 3A, that's 12W, or if you draw 6V at 2A, that's still 12W. So is 1V at 12A. For the most part, the amount of W is directly related to the amount of heat the coil will produce. Any coil that's powered by 12W will produce the same amount of heat, whether it's 6V at 2A or 1V at 12A. If the coil is bigger, that heat will be spread over more surface area of juice, and if the coil is smaller, that heat will be concentrated over less area of juice (hotter juice in a smaller spot).
Things start to get tricky when you consider that V and A are not entirely independent. They are related by the amount of resistance you are running the voltage through. If resistance is R, then A = V/R. So, given a fixed V (4.2V for example), if you halve R, then A doubles. Since W = V*A, if you halve R and keep V the same, you double A. When you're building with a mech mod, you have no control over V. Your battery will produce somewhere between 3.7V (or a little less) and 4.2V, depending on how fresh it is. That means if you want to adjust W, the only way to do it is to raise A by lowering R. So, with a mech mod, it might make sense to use a lower resistance coil in order to raise the total wattage. The question is not what wattage to run for a coil with a particular resistance, the question is what resistance is necessary to produce a certain desired W (and, therefore, heat). For example, if your battery is fresh and produces 4.2V, and you want to output 12W, you'd pick a coil resistance of 1.47 Ohms (12W/4.2V is 2.857A. To produce 2.857A at 4.2V, you need a resistance of 1.47 Ohms). If you want to output 20W, you'd pick a coil resistance of 0.882 Ohms (same calculations as above, just plug in different numbers).
For a variable voltage or variable wattage device, you get to pick either V or W independent of R, within limits. The exact limits depend on what mod you're using.
Things also get a little trickier when you consider that there are different ways of constructing a coil to have a target resistance. For example, 27ga kanthal is about half the resistance of 30ga kanthal, so you could make 5 wraps of 30ga at a particular diameter or you could make 10 wraps of 27ga kanthal at the same diameter and end up with about the same resistance. Or, you could make 5 wraps of 27ga kanthal at twice the same diameter, and end up with the same resistance. If you powered all three coils at 12W, you probably wouldn't get the same vape, because the coils are producing the same amount of heat, but they're spread out over the wick differently. Or, you could also make two coils using 10 wraps of 30ga and then run them in parallel (ohms law says that when you have two equal resistance coils in parallel, the total resistance is 1/2 the resistance of one of the coils). Once again, the two coils in parallel will produce the same heat at 12W as the other coils, but that heat will be spread over more wick, and having two separate wicks will also have a profound effect on how juice reaches the coil. So, same wattage, same resistance, but a different vaping affect.
These are ALL things you need to understand and play around with at safe and sane resistances and amps (like 1.5 ohms total) until you understand what affect they have on vaping before you start trying to increase your wattage. Try lots of different builds out at 1.5 ohms and see what works and doesn't work, and then if you still can't find something that produces the flavor and vapor you want, then maybe start gently lowing the resistance or raising the wattage. But, don't fix it if it ain't broke.