Loosen the throttle friction if you need to. The only thing I can say is try to lead with the throttle. In time it will become a habit.
As for the shaking. How often did the previous owner lube the machine? If he kept it well lubed, it shouldn't be a major issue. Many times the shaking is caused by the dampers. All you need is one damper tighter or looser than the others. Depending on how tight they are, they can get air bubbles in them and they have to be purged.
Since you haven't flown a helicopter in the last 4 years, I would strongly suggest that you get some dual in it, prior to going off by yourself. The machine does have a few quirks. And if you ue the Enstrom Program Insurance, you will have to do that anyway.
Good luck, I enjoyed mine very much.