Rail tickets from Osaka to Kobe...Should they be purchased in advance? How do I get prices? In English? Also need a clean, nice but not expensive hotel in Osaka...

Osaka to Kobe .
Its a 25 minute ride (if that) depending on the train.

Just go to the rail station and buy your ticket. Not expensive at all.. Have done it years ago when I lived there, but, the price is low.

With regards to hotels, try ths link.
http://www.toyoko-inn.com/eng/
Have used them in Shina Osaka in the past. Small clean rooms, but, these are Japanese business hotels

This is where I stayed in Shin Osaka .. 10 minutes walk or less from the Shin Osaka Bullet Train ( Shinkansen) station.

http://www.toyoko-inn.com/e_hotel/00016/index.html
http://www.toyoko-inn.com/e_hotel/00016/map.html

Check Hyperdia for timetables and fares. The Classic interface is better, IMHO.

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

Osaka to Kobe is about 35 to 40 kilometers.... Literally dozens of trains per day.

You can take the train from OSAKA station in the city to Kobe,and this is a regular service.

Alternately, you can take the Shinkansen ( Bullet train) from Shin Osaka to Shin Kobe. Its one stop.
No need to look for time tables.

Miss one train, and another is along in 15 minutes or so.