Hello there,
Bringing a normal suitcase on the Shinkansen is no problem at all. Between Osaka - Shin-Osaka, you'll be traveling by local train. Generally it's no problem to bring a suitcase, however you may have to stand in the area near the doors where there are no seats. The trip between Shin-Osaka and Osaka station is a couple of minutes anyway, so don't worry too much about it.
There's not much difference between staying in Osaka or Kyoto, both are fine. The real thing to look out for is the distance between the train station and your accommodation.
Hope this helps!
Daniel