My first steps in the gym

I have started doing some exercises at the gym since January at the gym (The time should be placed last or first because "exercises" and "at the gym" together form a coherent idea, splitting them apart by putting the time in between makes it hard for people to keep up with your message.) (that which my wife usually goes. (The one that my wife usually goes to/the one which my wife usually visits) ... she was the person one who encourages encouraged me to start doing this begin this activity) ("She was the one who encouraged me to start doing this" sounds more fluent) and I must admit that it was a great idea. Doing exercise is a good therapy to fight the large amount of hours that I (and the most part of most of the people who works sitting in a chair) pass watching the screen of my personal computer. In the beginning, all this gym equipment (dumbbells, bench presses or smith machines, among other tools) could frighten you, but in the end you will see them as part of your current routine's objects. Besides, if you take the daily routine of doing exercise, it Besides, making sports a part of your daily routine/including exercises in your daily routine will prove beneficial for your health and mood. (There's not much wrong in your last sentence, but again, I think this way it sounds more fluent.

Here's a different version of your text that sounds more fluent and consistent:

Since January, I started exercising/working out at the gym (The one my wife usually goes to)... She was the one who encouraged me to start doing this, and I must admit, it was a great idea. Exercising is a good way of fighting against the long hours that I (and most of the people who work in a chair) spend watching the screens of our computers. At first, all this gym equipment (dumbbells, bench presses or smith machines among other tools) could scare you off, but eventually you'll start seeing them as part of your current routine's objects. Besides, making sports a part of your daily routine/including exercises in your daily routine will prove beneficial for your health and mood.

Good luck with your English,

Best regards.