I was wondering if your level effects the stats on weapons and armor you find. I'm only level 15 but I want to grab some of the unique weapons in the game but I wasn't sure if I should wait until I'm a higher level?

In Fallout 4, level doesn't affect the stats of your equipment. You might find more powerful guns as you level up, but those will have the same stats at low levels as they would in higher levels. So go ahead and get those uniques if you can; they won't be any weaker than if you were to get them later.

Yeah, you can pretty much max out your first weapon and not have to worry about finding a stronger version of it. To my knowledge, they only get stronger with the selected perk. IE: Rifleman, Gunslinger, Commander? Etc.