Welcome to the boards, therock. We're glad you're here.
I have a 7mm Asha Asscher solitaire in F color. MissCassie is right -- it's VERY white and between that and the step cut, it does tend to look glassy to me. The people around me told me the same when they saw it. But still, there will be others who feel differently, as this type of thing is all in the eye of the beholder.
So I personally say go for the H. I often wonder if I'd like one in a J, but I think H is the farthest they go for color, isn't it?
I'm glad you're prepared to clean your ring.

Asha is a material that requires frequent cleaning in general, and then when you add a step cut you need to clean it all the more because every little thing shows. You'll likely need to do it every day to keep it looking nice.
As for longevity, that's a mystery to most of us. Some people wear their Ashas for several years and are very rough on them, and the stone still looks great. Others baby their ring but need to replace the Asha after only a year due to visible scratches. Most people fall in the middle somewhere.
I wore my Asha for six months and babied it quite a lot -- no household chores, weed pulling, etc. But I did accumulate several small chips on the top, at the edges where the table meets the crown. I think if I'd kept wearing it, it would have been obviously visible enough to bother me at about the 1 to 1.5 year mark. So I quit while I was ahead and set it aside with the intention of setting it into a pendant where it will last much longer and I'll get more enjoyment out of it.