Equipment to use for at home workout

I’ll go to the gym and do only specific machines like elliptical, arm and leg machines and use the “yoga” Mats there for abs.

But for what I’m trying to accomplish which is losing back and arm fat, and getting a bigger butt- those machines are usually surrounded by the big guys and I got anxiety as it is so I’d rather not go over there. So instead I’m trying to do it at home.

What workout equipment do you think id need? Like I have a dumb bell/other weights , yoga Mat, And a bench press thing my dad uses (idk what it’s called). I’m planning on buying a resistant band for butt / leg workouts but I don’t want to waste money and stuff that might not even need.

Also is there anyone you’d recommend I follow/ watch for guides on YouTube or insta or something??

Side note- I’m really uneducated. What workouts reduce arm size cuz my arms are fatty w no muscle but I don’t want my arms to get bigger. Just smaller and built w muscle not fat if that makes since. Also same thing with my back. I’ve never had to target these areas before so idk