Looks like you're pretty close to the answer already! You should use "normalize(target - position)" though (rather than "position - target") so that the player moves towards the target, not away from it.
The player then accelerates in the direction of your "steering" vector. For this you'd write something like
velocity = velocity + acceleration * normalize(steering)
where "acceleration" is the amount by which the player's velocity can change in one turn.
Be warned that this approach may have some odd side-effects! In particular, the player may go into orbit around the target! With a bit of experimentation (and, possibly, some friction) you should be able to make it do what you want though.
I hope that's some help. Apologies if I misunderstood your question.