An all round good fishing light rod?

I think you will have trouble getting a single rod that is suitable for lines of 3lbs and 10lbs. A rod that is right for 3lb line will have a test curve of about 12ozs to 1 lb. For 10lb line then a rod with about 2lb 8ozs test curve would be ok. If you opt for the heavier test curve you will very easily break the 3lbs line and if you pick a rod suitable for 3lbs line then you may not be able to use the strength of the 10lbs line without risking damaging the lighter rod. You could get a quiver tip rod (as you have mentioned) these have as many as 4 tips and at a pinch could be used for float fishing. Shakeapeare make good rods and are usually easy to buy at your local tackle dealer, if you do more float fishing then a rod of 13 feet (3.9 metre) is very popular. As far as reels go, I would buy the best Shimano or Diawa you can afford, both are good.