I'll add to the excellent advice above...
I have an Iridium satellite phone at work and for a no minute monthly plan it's about $45. Air time is around $1.55 US per minute. I rarely use it, so this is an acceptable plan for me. If I were to use it more often, you can purchase plans that include minutes, but they get pretty expensive.
The phone is a Motorola 9555. It's a satellite only phone, and while not the newest model, has a good track record. The phone, new, was about $1500. That included a lot of accessories, such as charger, external magnetic mount antenna, case, handsfree cord, etc. Due to the price of the phone and it's intended use as an emergency option, I purchased a Pelican 1200 case to keep it all in. Since it occasionally gets loaned out, I wanted a case that everything went into and was kept together.
As for the air time plans, you need to figure out if you want a USA phone number, or if you are willing to use the carrier assigned number international number. The difference depends on if you want those calling your satellite phone to be able to call you via a less expensive route, or use the international calling route. There is a cost difference, but I can't remember what it was for my phone. Since I use it for calling out, I went with the cheaper international number.
I'd second the advice about renting. Unless you need to have one in your possession all the time, it might be an easier route.
Also, you don't get your service directly from Iridium, you buy it for a reseller. I'm using SatWorx, and have had mixed results. I pay via a purchase order, and they can't seem to properly bill us consistently. I'd say shop around, the prices are all pretty much the same, but what you get from them is slightly different.