I was wanting to go on the 3 day tour some time in 2017 and had a question or two.

When you meet in Kiev and then head to Chernobyl do you take your suitcase with you or do you check into the hotel prior?

Is there any chance that something could get contaminated even if it never touches the ground? Can your shoes get contaminated?

You will be staying at a hotel in Chernobyl, so you need to take all your belongings with you when you are boarding the tour bus in Kiev. You will check in during the first day of the tour.
If you follow your tour guide instructions then one of your things will get contaminated (including the shoes).