It's tempting to want to be seen as a jack-of-all trades. The seemingly obvious thing to do is to broaden your skill set to make yourself more marketable. Surely that must mean you're more skilled and make you more desirable to potential clients or employers, right? I would argue against that mindset.
You need to focus on one area of design, especially if you're just starting out. That could be web design, illustration, branding, whatever. Pick one thing and stick with it. It sounds limiting, but that's the point. Every new thing you try to add only takes away from what you should be focusing on. You can't give 100% of your time and attention to everything, so you need to find that one thing you can focus on.
Think of how your computer slows down if you've got too many applications running. The computer slows down and can't perform its best because it's trying to do too many things at once. Like a computer your brain has a finite amount of resources to work with, and the more you try to do the less optimal your work will be.
Taking a step back from the nerdy metaphor (I couldn't help myself), if you focus your work in one area you will be able to maximize your time and attention for that one thing and get even better as a result. Rather than being pretty good in multiple things, you will be great at one thing.
"But won't it hurt my image if I don't show variety in my body of work?"
If anything focus will improve your image among the type of people you will want to work for. They'll see you as an expert in whatever it is you're focusing on. Think of the different kinds of lawyers out there. There isn't a lawyer who does every type of law. There are real estate lawyers, copyright lawyers, environmental lawyers, the list goes on. They have specialties, and they are seen as experts in their respective fields.
If you already know what you want to focus on that's great! But maybe you're still trying to narrow it down, and that's okay too. Your focus should be the thing you love the most, something that you feel like you can take to a level beyond your other interests. In most cases it might be the the area you're stronger in because you've already been giving it a little more attention.
Remember though that you don't have to be stuck forever. There's always room to add to your repertoire down the road, but for now; focus.