That would be the best
. But I hear what you're saying. Shoes are expensive and important. You might want to try on several pairs and look online, as you can often find them cheaper than in the stores.
Also, ask a salesperson about last year's model or color. I just bought tennis shoes for my son and paid $45, down from $109, because the company had just come out with a new color scheme for the same shoe. Nikes, no less.
That aside, it's hard to make a choice. As you know, they are really very different shoes. Cross trainers generally give you a little more support, while running shoes are more flexible and focus on the forward motion of the foot. I think you can run fine in cross trainers, but they may wear a little quicker. Cross trainers are helpful if you have something with a lot of lateral motion; I don't know if your fitness class falls into this description.
I have two pairs of Rykas and I really like them. The first pair is a pair of cross trainers that I've had for quite some time. I did a bit of treadmill in them but once I got more into running, I got some Ryka running shoes with a gift card from the holidays. They are both very light and very comfortable. They also seem to hold up pretty well as compared to other shoes.
Just checked Kohl's website; they have Avias on sale right now and you really could get a pair of each for what you want to spend, if that brand is comfortable for you. My husband has Avias and he likes them.