4G radio module is not that big anyway. Battery is the largest component inside iPad. To make iPad slimmer, you have to cut battery life.
I could see $299 for the WiFi model, more for the 4G/LTE model. Unless the cost really works against it, I'd guess retina display included, to trump the Nexus and Kindle Fire 2.
If "only" the 1024 X 768 is available, I'd guess the price would be close to $199 (since the Nexus and Kindle Fire 2 would have higher resolution).
An iPad mini the same price as a Nexus or Kindle Fire 2 would smoke them both. But Apple probably wants to leverage its supply chain edge for retina displays if possible.
I could see Apple releasing a WiFi iPad mini before the holidays, and an LTE version early in 2013, if as Technarchy notes, the battery permits. The iPhone 5 will probably be released this autumn, plenty to keep the LTE front occupied.
Dchao's point about Amazon content quantity edge is important. Amazon also has the solid-merchandise-delivered-to-the-door edge. The collision course between Apple and Amazon is going to get more obvious.
I don't think Apple is worried much about an iPad mini cutting into the iPad3 market. Even if the iPad mini becomes the hot seller, Apple will have great margins on their 32GB & 64GB minis.
Many people have overlapping Apple products, a sort of one of everything from the iPhone to iPad to MBA to iMac. I believe Apple has a clear roadmap of how to sell customers multiple sized devices and keep functions different enough to drive sales of each. They are delighted that the intermediate market is open between iPhone/pod & iPad. Tall venti grande. They are even better prepared than they were at the start of the iPhone & iPad, so it will be a more mature (superior?) product at the start.
It's all interesting to think about.