Osaka to Arima Onsen, then to Tokyo

I'll be in Osaka for a few days. I'm planning to stay one night at Arima Onsen and then travel to Tokyo.

1. How can I go from Osaka to Arima Onsen, and then from Arima to Tokyo(on Shinkansen)?

2. I'll have a big suitcase with me (doing lots of shopping). How will this affect my travelling plans?

Thank you.

How can I go from Osaka to Arima Onsen, and then from Arima to Tokyo(on Shinkansen)?

You can take a direct bus from Osaka to Arima or trains via Kobe. A further, more time consuming approach is by cablecar and ropeway over Mount Rokko. The access methods are explained on the following page:
http://www.japan-guide.com/e/e3558.html

From Arima to Tokyo, you could take the bus back to Osaka and then take a train, plane or bus to Tokyo. Or you could take trains to Shin-Kobe Station and take the train from there to Tokyo.

Travel options between Osaka and Tokyo are expalined on the following page:
http://www.japan-guide.com/e/e4006.html

I'll have a big suitcase with me (doing lots of shopping). How will this affect my travelling plans?

It will complicate them. You will have to come up with a strategy how to deal with the suitcase. Basics on how to deal with it are explained here:
http://www.japan-guide.com/e/e2274.html