Most popular is sailmail or airmail on ssb. Advantages of sailmail is it's nearly free, doesn't require a ham license and you can conduct business. Airmail requires a GENERAL ham license (US), is totally free but no selling of stocks, moving money around or any other business activity. It's amateur radio rules. Many use both sailmail and airmail, if they are properly licensed.
Some are using Iridium phones but cost here is a major factor and many use it just for phone calls back home, using sailmail for most correspondence. It doesn't replace the need for a ssb as you will want the information from the nets and be able to call or respond for help to boats IN YOUR AREA. The phone won't call the people on scene, or get you the local information. Reporting on the net will be a daily ritual for you and that means ssb. A sat phone is an enhancement to your communications, not a replacement.
I've seen a few Inmarsat antenna's on boats but they are very few except on the larger yachts. Same restrictions as the Iridium phone, cost and not being a replacement for a ssb unit. Not sure how good the systems are today but, regardless of the big antenna, they also require a terminal, space hard to find on a cruiser.
There is no BROADBAND solution, no matter what you choose. Data rate is 2.4 kbps for Inmarsat and (I believe) 9.6 kbps for Iridium. You will not be surfing the net without a large bank account.
A`ohe `ulu e loa`a i ka pokole o ka lou.
No breadfruit can be reached when the picking stick is too short.