Everything you need to know is on the CASA website in the DAME manual - although it can be hard to find.
Firstly, I have been in the practice of getting a class 1 every 2 years. This is no longer a good idea because CASA treats it as a medical lapsed for more than 3 months and it goes for internal review. If you get your class 1 at the time your class 2 expires, you might find yourself not flying for a month, because the DAME is not supposed to give you an extension to the class 2 if you are going for the class 1.
Initial issue of a cpl has a bunch of tests that the renewal doesn't. Top of this list is an eye test with a specific focus on glaucoma. So its the drops in the eye don't drive home deal.
You will need a hearing test, although some DAME's can do it.
You will need an ECG. Either resting or stress. The DAME may do resting ECG, but stress ECG's are always done somewhere with resuscitation capability. Typically at a cardiologists rooms at a hospital or day surgery. I believe there is a significant incidence of heart attacks during stress ECG. Don't worry - it will be a breeze for you. The CASA test is less severe than many.
You will almost certainly need a blood test. Results will typically be 2nd or 3rd day.
Its determined if you need some of the tests (ie stress ECG) depending on risk factor. There is a chart that looks at weight, smoking, blood pressure, cholesterol, etc to determine what you need. Stress ECG will need to be booked some time in advance.
Very few doctors will take unsolicited phonecalls. They have no time and will almost certainly have a patient sitting in their rooms if you get put through. But most will call back if you leave a message. I'd call and tell the receptionist you want to understand what tests you require and request a call back. But, do your homework about what you want to ask first. You will probably be one of 20 call backs. The doctor is very unlikely to want to chat.
I'm married to a doctor and we have a pathology lab as a tenant, so I tend to do everything before I go, but I don't care if I do extra. I think its a bit arbitrary which you do first. I would be very very surprised if you pay a fee twice. In fact, you may not need to return to the DAME. They all get results electronically now. He'll just match the results he is sent by email to your file.