Muscle gain and fat loss being mutually exclusive is one of the most ridiculous and damaging fitness myths out there imo. To answer your question, yes, you can most definitely get big and strong without getting fat. In fact, in all likelihood you will get leaner.
Just follow the basics and focus on big compound lifts. Bench, squat, dead lift, shoulder press ect.
I'm right there with you in wanting to look good naked in the mirror...nothing wrong with that in the least.