Best ODE algorithm to use for time/velocity independent potentials?

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Hello, I am not sure if this is the right place to ask this, but I don't readily see a "numerical methods" forum here so I assumed this would be the place to go. Sorry if I overlooked another place to post this!

Anyway, I have some points interacting via potentials that are dependent only on distances (IE, not time or velocity), and I am wondering what would be the best ODE algorithm to use to simulate the motions of these points. The number of interacting points is fairly large, from 150 to 300. Let's say they're interacting via an additive pairwise potential similar to Newton's law of gravitation.

What would be a decent ODE algorithm to use that is both fairly accurate (and not subject to huge error propagation) and not too complicated for solving the equations of motion?

Any help would be greatly appreciated.
 
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Is RK4 noticeably better than, for example, Beeman or velocity-Verlet? I've never used RK4, though I know it's the word for many people. I don't know much about it. Right now, I'm using Beeman for energy conservation, though what I'm most interested in is accuracy of trajectories. Would RK give me a bump up in this category?

Thank you in advance!