What makes a good/great first hole?...
First holes rarely, if ever, "define" a course, but should they not offer signals as to what lies ahead?
Like you I believe it should be an "invitation" as to what to expect for the rest of the round. I'm not into opening holes that are either the hardest nor the easiest on the course as their main aim should be to get the field away.
For this reason I'm also not really into P3 openers (I am yet to see a really good one ?) or those that are heavily penal or blind. I do have a liking those with an elevated tee as to give somewhat of a panoramic vista of what lies ahead.
Also, I like to see a subtle strategic interest of some sort - not over the top but something that 'tests' the ability of the player first up.
In the UK - the 1st at St. Andrews is one of my favourites. A wide fairway with OOB not really in play but it's visually there and the burn to test the player especially with the pin at the front
I also enjoyed Ballybunion (Old), Saunton (East), Rye, St George's Hill, Royal Porthcawl for their elevated tee positions and Prestwick and North Berwick for their subtle strategic tests.
In Australia - some of my favourites include - The Lakes, Portsea, New South Wales, Horsham, Victor Harbour for most of the reasons aforementioned.