My experience is that the soil can be fairly rich, but the most important thing (besides lots of sun) is fast draining. Irises don't like wet feet - that's what causes rot. Also, be sure that the rhizomes are about 2/3 about the soil, only a bit in the water. As someone once said to me: think of a duck on the water: the rhizome is your "duck"! The roots under the rhizome go in the soil.

They also rot more easily when they are too close together. Be sure to leave 18-24" between each rhizome.

As shapiro said, drainage is very important. If your clay is the type that responds to addition of gypsum, then that would be top priority, as it helps to open up the clay particles and improve drainage. Also raise your beds as much as possible. Addition of well rotted cow manure and compost will help bulk up the soil, but will also increase water holding capacity and acidity, so lime is also an essential ingredient.
Dig well to open up the soil to a good depth. In clay soil rhizomes should be planted fairly high in the soil, but this can also result in wind rock problems where rhizomes are not fixed into the soil firmly, and cannot establish good root contact with the soil. Even though I have clay soil, I prefer not to have the top of the rhizome showing, and make up for poor drainage by raising beds up to 12" above the surrounding garden.
The ducks out of water rule also does not apply in areas of sandy soil, wherre the rhizome can be even 2" under the soil surface and perform well.
Here in Australia, rhizomes growing at surface level can burn in our intense heat of summer.

RHIZOME IS YOUR DUCK.!! Love it.!!! that will come in handy in tomorrows planting of MY first TBI bed. Thanks for insite! I feel so smart now.!! Great piece of advice for a newbie to TBI like me. Thanks for sharing your knowledge! much appreciated:)

Thank you for the responses. Much appreciated!

I expect that, once done, I will have raised the level of the bed by a minimum of 6-8", maybe more. I'm still struggling with WHAT to use to raise it, however. Most of the landscape material providers here have little in the way of "specialized" soil. It's pretty-much topsoil or compost.

I'm trying not to go to extraordinary (and backbreaking) lengths to create my own mix, so I'd prefer to find someplace where I could get 2-3 yards of material that could be used as-is. The topsoil seems like it would be too heavy, and the compost too rich... although a friend has used the compost and says it works fine. I'm not so sure.

The "clay" soil I have is not very "clay-ish" - I've seen a lot worse than what I have.

My only other option is to buy bags of topsoil/compost/peat moss/sand and mix my own. Anyone here ever do that? Is there a "recipe" of sorts?

Thank you all again!