I'm not trying to troll or be mean spirited, but take it for me, any EQ mount that is in the price range you are looking for is going to drive you absolutely bonkers...at least in the 'motorized' category. You can get close to the upper price range on a manual EQ but it would only be good enough to piggyback a camera. I have been in the hobby (astrophotography) for about 10 years now and have lived through the pain of the cheaper mounts. Unfortunally, cheap mounts are only good for one thing...making you so fed up with them that you eventually get tired of trying and give up....and keep you from actually watching the shower since you will be constantly messing with the mount.
For what you seem to what to do from the summary above you could accomplish with the following
:
1. Stick the camera on a normal tripod and aim where the meteors are originating from with the widest angle lens you have.
2. Take 10 sec shots after ten second shots with an ISO of at least 800, while adjusting for position every 10 or so minutes so that you keep the general area of the sky in view.
3. The next day, use an astrophoto stacking program
RegiStax to 'stitch' together your images made the previous night.
You would be surprised how good the pictures will actually come out...and for the price of a $50 tripod.
Now, barring that you are dead set on an EQ mount for this, I have only one piece of advice. In the land of EQ mounts, the heavier the better (less shaking, better stepping motors). And the heavier it is, the more expensive it is. There is just no getting around it.
I currently have this
mount and it required a complete tear down, polishing, and rebuild before it was even capable of astrophotography...and that's at $600!!