You have definitely asked a question that is a huge controversy, at least in my neck of the woods. But, my recommendation follows pretty much what Chris has stated.
If you are in no hurry and can spend some time in the field, then I would do that. Not only will it make you a better paramedic in the end, it will also help you to get a job. As to getting your AEMT, I actually think it might benefit you although I got my intermediate 1 year prior to getting my paramedic and only used that level 2-3 times. That being said, it was 2-3 times more than had I not. Not to mention, I would not have passed up taking the national registry which made going through the skills testing at a paramedic level less traumatic.
I also recommend you get as many of the pre-reqs done up front. You will find the program to be a little to easier to understand/comprehend. (I had my Math/English completed, but struggled with doing pharm/A&P as co-reqs).
As to how long to stay at the basic/intermediate level...only you can determine that one. I spent 2 years as an ECA before moving to Basic. Spent 2 years before becoming an Intermediate. So, by the time I graduated the program, I had 6 years under my belt. Now, I've been a paramedic for 1 year but I have 7 years of service.
I think it's fantastic that you are looking at what will make you a better medic and less at how soon you can get a paying job. It's good you are in a position to make that decision.
Good luck on whatever you decide.