Thanks everyone for your input. More than anything, it's been really great at making look at the bigger pricing picture.

My conclusion:

I'm not going to put in a free tier, because as @brudgers mentioned below, if they can't spend $1.99 to try it, then they're not my target market.

So, in words I read somewhere else before, instead of downgrading my product, I should upgrade my customers.

I will instead spend time creating a high quality product.

And slowly raise prices as I improve the product.

Thanks again, everyone.