The main reason that most people go to the gym is to gain muscle/strength and lose body fat, whether they are aware of it or not.
This is sometimes described as 'toning up', 'getting fit', 'building lean mass' etc. They're all just synonyms for essentially the same thing, and the process that results in this happening is more or less the same as well.
The process is 1) get big and strong, and then 2) cut excess body fat. The problem is that many people think that they can do both at once, or do these in reverse order.
When I explain this to people though, I'm often met with a face of concern and a statement about how they don't want to get too big or bulky.
For anyone who has been training for any amount of time, they'll realise how funny this is. If gaining muscle were that easy, I'd look a lot bigger than I do after TEN YEARS of lifting weights. Instead I just look like a guy who does a bit of training in his spare time.
The best analogy I can give to you for just how absurd the concern of getting 'too big' is, would be to liken it to someone looking for a new job, but being worried that they'll find something that pays too well. After all, well-paid jobs are a dime a dozen and life would become really complicated with all that spare cash floating around, right?
Getting 'too big' is like getting 'too rich' - it can happen, but it's not going to happen to you.
I'd strongly suggest you forget about cutting bodyfat until you can do the following:
2.25x bodyweight deadlift
2x bodyweight back squat
1.25x bodyweight bench
0.75x bodyweight overhead press
15 strict pull-ups / chin-ups