rattling/vibrating noise when I go through 1st to 2nd to 3rd gear

A lot of rattling/vibrating noises are caused by loose exhaust heat shields. They can sound pretty bad at times, but aren't a big deal. Usually a couple hose clamps will fix them right up. otherwise a tech needs to check this out and identify where the sound is coming from.

how many miles on car?

In addition, do you hear it when stopped and reving engine? Possible cat conv problem, see answer #2. Either way there is a problem that needs to be looked into, especially if it has 'any' warranty from the seller, before it runs out.