I ordered Mr Shield's 3-pack of screen protectors on Amazon and they fit pretty well. I pre-ordered the official transparent shell but it doesn't come out until May 30th.
In the meantime, I had ordered this case, which happened to arrive the same day as the phone. It's kind of a pain to put on but once in place, it feels very sturdy but makes the phone quite bulky. I only plan on using it when I'm out hiking or doing activities in which I'm more likely to drop the phone.
As for arm bands, I had one for my old GS4 and it fit in there okay (stuck out of the top), but the velcro isn't sticking too much, so I just ordered another one for the GS5, figuring it should fit the Idol 3 too (might stick out a little as well but that doesn't bother me).
bought this one as someone else posted http://www.amazon.com/LK-Protection-Shock-Absorption-Resistant-Protective/dp/B00WMO0HS2
and I'm also thinking of getting this one. http://www.amazon.com/IDOL-5-5-inch-Case-NageBee/dp/B00WL2LPB8/ref=lh_ni_t?ie=UTF8&psc=1&smid=A2JWBJUIPNSXAJ