Hi Hierophant.
I'm a member of most of the additional Orders over here, which aren't arranged quite the same way in England as in Texas but are essentially equivalent. Most of them are very interesting rituals with very good lessons, and I enjoy them all.
Nevertheless, I think Ashton makes a very good point, there's plenty to think about in the Craft degrees. No need to rush into any of the additional parts. I did: I went rushing in, and actually it was too much too soon. I found myself wishing I'd left a few things until a few years later. Since you haven't taken your MM yet, I'd say don't worry about the additional Orders yet, spend a year or two thinking about the Three Degrees first, and then think about exploring further. Patience is itself an important lesson!
Just for comparison, the English system places much more emphasis on the "York Rite" than on the "Scottish Rite" (although that's not what we call them), so almost everyone here joins (at least some parts of, and sometimes all of) what you'd call York Rite first. To me our system makes sense ... but of course, that's simply what I'm used to. You have a differently-arranged system, so your mileage may vary, and my sequence isn't relevant to your choice.
T & F,
Huw