The different verlets are all pretty good, they just have differnt pros/cons. Velocity verlet better balances the precision between velocity and position. Presonally I like velocity verlet because it gives you an explicit velocity term, which is useful in a number of situations, like collisions (don't let the propoganda for vanilla verlet fool you. You need to explicitly set the velocity after a collision to get correct results, even though the formula uses an implicit velocity term!)

The Theory of Molecular Dynamics Simulations is an excellent article. In general, molecular dynamics simulations seem to be a step ahead of game physics, even though they're doing basically the same thing.

And to save you a step, you'll eventually want to know how to respond to collisions correctly. The coefficient of restitution is an article I wrote to address that (see the "use" section in particular).