Any health concerns from this kind of thing are probably the kind that build up over time like repetitive stress injuries unless you spike your body with grams of caffeine. Sitting down for 24 hours is not a massive health risk.
I agree with the suggestions above, like take breaks every hour (at least two minutes, so you can rest your eyes by focusing on objects at varying distances). Movement is also good. If you want more gaming in your marathon session it might be fun to do a variation on Turing chess, especially since DF will progress in real time. Make sure to stretch your arms, wrists, and fingers at regular intervals and don't go straight from sitting to a strenuous activity without warming up a bit.
Avoid caffeine; in high doses it can have pretty negative effects. In any dose it will dehydrate you, which along with sitting and repetitive motion can give you muscle cramps and spasms. It can also exacerbate any heart or circulatory troubles you might have, even if you aren't currently aware of any. The same is true of energy drinks Gatorade isn't much better than any other sugary drink if you're not sweating for >30 minutes, but won't hurt you.
For food, go easy on salty items and be careful not to overeat.