I agree with everything Deborah has said. Just going to chime in here too.
To my knowledge, the reason for the calorie difference between "male" and "female" in formulas is simply due to the fact that the average "male" has a higher lean body mass than a "woman". Lean body mass= muscle. Muscle requires more energy to maintain, therefore resulting in a higher caloric need.
Generally in a "bulking" phase, meaning trying to gain weight/lean mass, you should aim to consume about 500 calories over your total daily energy expenditure. This would have you gaining about 1lb a week, which is usually the recommendation. As Deborah said, monitor your weight and make adjustments as necessary.
But remember your weight will fluctuate day to day, and even throughout the day. Try to only weigh yourself once a week, and always first thing in the morning before you eat or drink anything.
You WILL gain some bodyfat when eating at a caloric surplus, it's unavoidable. The amount of lean mass you also gain is entirely dependent upon the quality of your diet and how you're training. Diet is the most important factor however, so if you want to make quality gains, you're going to have to opt for less fast food.
Again, like Deborah said, gaining muscle takes a LONG time.. you will not see drastic physique changes in a month, two months, etc. and will likely be six months of consistency before results become noticeable.
Having a personal trainer is a good start, they can probably teach you the foundation. I also recommend just reading as much as you can, and there's a plethora of helpful videos on youtube as well. Plenty of free information out there on the internet... just don't believe anything that tells you that you need any sort of supplement to make muscle gains. You don't, not even protein powder, although it does help you achieve protein intake much easier.