Public health insurance is probably the better choice for you, but it depends on a few details. With €2000 - 2500 monthly, you'd pay around 8 - 10% of your income as contributions to statutory health insurance (GKV) as a freelancer (so roughly €160 - 250), where you cover half yourself and theoretically can deduct the other half as a business expense. That's usually cheaper than private plans, which might look tempting at your age and health status initially, but get significantly more expensive long-term.
What was mentioned in the previous answer is important: look into the Artists' Social Security Fund (Künstlersozialkasse/KSK). As a graphic designer, you might be able to become a member there - then the KSK would cover part of your contribution like an employer would. That would lower your costs even more. You'd still need to register with a health insurance fund, but with this subsidy. Check with the KSK directly whether you qualify - the requirements aren't straightforward, but it's worth checking out.
I'd only go private if you're earning significantly more and you know you don't want to switch back to GKV long-term. Private health insurance is cheap now, but later it becomes a real pain with the costs. You can register with GKV basically anytime - just do it with a health insurance fund of your choice.