Just bought a Shimano Stradic CI4+ spinning reel, moved handle to right side and while reeling felt odd. While holding reel can feel and see handle movement back and forth like loose in the housing. Is this normal on Shimano reels? (1st one bought)

Mine isn't like that at all. It's good tight and smooth. 

Return it.

Sometimes when you take the handle off the pieces of the handle will loosen up. Not sure what it's called but the round piece that presses against the reel body will unscrew a little from the shaft. I had it happen a few times. Just take the handle off and make sure its screwed together tightly.