Lots of little help so far. Let's see if I can change that.

The best source of information on rail options is Hyperdia. I'll give you the link.

As for fastest or cheapest, it depends on where in Osaka you will be staying. There are a number of stations from which you can depart. Assuming you will be near the main Osaka Station - which is not necessarily true - the local JR Rapit Service is cheapest, 540 yen and about 1/2 hour.

http://www.hyperdia.com/en/