Hi there! I know this is an old thread, but my recent experience is relevant so thought I would share!
I just did a frozen IUI. I chose IUI because, according to The Sperm Bank of California Insemination Methods and Outcomes, IUI is twice as likely to be successful.
The trick with frozen IUI is timing it correctly. The reason some people prefer fresh sperm is because it lives a lot longer so you don't have to be as precise with timing. Frozen sperm only lives inside the uterus for 6-12 hours, and as a result if you haven't od'd an egg in that time you won't conceive.
Personally- I started tracking my ovulation the month before I tried (since you have so much lead time I would track it for a few cycles). I knew that I ovulated the night that i had a positive on the OPK because I had very strong ovulation cramps that woke me in the night (thank you body!).
I did an unmedicated IUI with a midwife who came to my home. Because I suspected I would ovulate in the middle of the night she arrived just before midnight and did the IUI the same day I had my LH surge. She did it in my bed so I wouldn't have to move and I could go to sleep after. When she did it she complimented me on my timing as my cervix was in the perfect position for it. The IUI was completely painless for me and I didn't feel a thing.
I was so worried I'd timed it wrong and that I should have waited til the next morning so I knew the egg was waiting there. The 2ww was really stressful.
It worked out, however, as on day 12 I had my BFP!!
Just fyi- I used The Sperm Bank of California. I really like their low family limits. It turns out that my donor only donated for a very short period of time and so not many vials were released. There is a chance I'll be the only pregnancy from the donor or there will just be a couple of others, which is kinda unheard of in the world of buying frozen sperm.
Anyway- good luck with your journey!!! I wish you as much luck as I had in trying to conceive. I'm really lucky because I feel such strong pains with ovulation so I knew when to time my IUI. I hope you have as much luck in timing it!