Your choices are limited by the radiant heat ... make sure that the installation directions and the product specifications say that it's OK over radiant heat.

Then pick from what's left.

basically - light or dark? Strong grain or little grain? Lots of bariation in color versus little?

Thank you for the response. My builder and some radiant floor ppl have told me as long as it is not too wide any floor will be okay. The thing is I am just not sure what I want in terms of light dark, I think maybe not grainy vs grainy-- ugh it is just so hard for me to look at a small piece of it and picture how it will look in a whole house! Do some stores have big displays?

I just got samples of white oak and of birch. I do not like the oak. The birch is ok but probably too yellow.
I also have smaples of American cherry. I LOVE how it looks when it is new before it darkens. But I know cherry darkens a lot and gets orange red and I do ot like that look for floors. Is there anything that looks the way cherry does before it darkens? I want to go with unstained, btw.

Consider Maple. It is much harder than birch and clearer than oak.
A smooth finish will show every scratch whereas a handscraped or distressed finish will obscure wear. A factory applied aluminum oxide finish is more durable than an on site polyurethane job.

I have to admit to being prejudiced but I like White Oak. I like the color in general and the significant variations in color. It can be finished anywhere from white to black so it can be changed to suit different decorating schemes. Unlike Maple, it has surface texture so it will not show scuffs and scratches as readily. If you can afford it, I would recommend looking into rift and quarter sawn cut. It's more stable and doesn't have the prominent Oak grain that many people dislike.
I have seen there are two types of Birch, red and yellow. Both seem to look good in natural color. I have stained some Yellow Birch successfully. Red Birch seems to be rarely used for flooring. Beech looks very similar to Yellow Birch but has a slightly more red cast and I've read it's less stable than Birch or Oak.
It's not necessarily a reason to pick a certain floor but since I do it for a living, I often consider whether a product will be available in the future. Picking something that you can find in the future might be vital if you have any damage or decide to do an addition or alteration.

If you like the color of American Cherry but want something harder, look at Cumaru or Amendoim. Neither darkens as much as the Cherry.

What about Dark Walnut colour for a smokier, more brownish look? I'm a fan of that: http://www.kustomtimber.com.au/our-range.html

Here is a link that might be useful: My Site

I am looking at red birch now-- the photos look beautiful but I still need to get a sample