Too many supplements can actually harm your body. A healthy diet, exercise and enough sleep are the best things you can do to help your immune system (+ having the important vaccinations).

There are a few things that can be supplemented if you don't take in enough on natural ways. But those should first be tested by a doctor before you start supplementing!

Vitamin D is often an issue, I take supplements myself. Iron is usually more of a problem for women. Calcium and magnesium can also be taken as supplements.

Vitamin C supplements are usually unnecessary as 1-2 glasses of orange juice a day (for example) are already enough vitamin C.