I have learned a lot and improved my technique (and the quality of the results), and a few of you have asked me to share the process, so I put together a few tips.
This is what I have found that works for me. I am sure there are other ways that may be better, easier, more polished, but that is one of the best things about the internet, we can keep learning as we go!
I have been using "Totally Stable" iron-on tear away stabilizer. I picked it up at a thrift store, but I have seen it at Jo-Ann's etc. The instructions are very confusing to me and I think they are geared more to machine embroidery, so I just developed my own process. (honestly, I think wax paper would work, but I haven't tried it)
I use a non-adjusting hoop, because I don't have an adjustable one that is small enough for the tiny shirts. I don't push it down all the way, because that stretches the fabric. An adjustable hoop might be easier to work with, but I get along with this one pretty well.
Please let me know if you have questions. When I write processes or procedures at work, I usually ask someone to read through it and see if it makes sense, but The Mister has gone up to bed already, and the kitties are not interested in helping me!