Hi Kristin,
Yes, I would put a blanket or something on the floor to protect the mattress and in the short term to test things I think this would be a good idea if you have the room.
If you then decide to purchase a rigid foundation (which I think would be a good idea regardless) … then I would go with something that was a little higher quality.
There are several posts which go into some detail about the different foundations (including several wire grid options) and you can read about them in post #7 and onwards in this thread, along with this thread and post #47 in this thread. I would choose one that had the best combination of price, and the most supportive surface with the least flex (unless you go in the direcion of a tension adjustable base which may also be an option if some of your tweaking or testing shows it may benefit you).
Step 1 = floor for a few days or long enough to see a pattern rather than just one nights experience 
Phoenix