I did a quick search, but most of what I read was dealing with aftermarket shifters etc.

My car is 100% stock, I notice around 4000-4500rpm the shifter vibrates while driving under load and in neutral if I bring up the revs. Also not sure if this matters but the shifter moves around while it's in gear(left and right).

Just wondering where I should start looking.

 

It's possible you need new linkage bushings. They are cheap and easy to replace.

 

Shifter movement can be caused by worn engine mounts. Could be the rear engine mount.

 

This ^^^.

Also the bolt/nut might just be loose. If that's the case, the problem may be solved simply by re-tightening the nut.

When replacing the bushings, the tough part is getting the old plastic bushings out of the hole in the shifter. There's precious little room to work, and they're often stuck in there really good. Needle files and dentist's picks help quite a lot. And you MUST drop that heat-shield!

 

years ago when i replaced those bushings on my old civic the bushing was busted so bad it fell out as soon as i disconnected it from the shifter. not much room to work and get leverage under the car so i took the rod out completely.