GRPS/3G smart phones using IP
For such handsets you can use IMAP or POP3. IMAP provides the cost benefits of your only having to pay for actual emails you download. You don't have to download your whole mail box before you can see an email. This is particularly of interest when someone has sent you a 10MB file and you only want to lookup a small email, say the address of the customer you are visiting.
Using GroupMail through IMAP allows you to keep the email on your phone and the mail in your mail box synchronised as emails you sent on your handset can automatically be stored on your GroupMail "Sent" mail box.
GroupMail and satellite phones
Satellite phones service (Inmarsat, Thuraya) providers offer a 9.6Kbit service and allow you to download your email using POP3.
The problem with this is when someone sends you a large attachment. With GroupMail you can set rules so that larger emails are moved from your inbox to another folder. Once a week you can connect using IMAP and review any large attachments to see if they are of interest.
Operating in this mode allows you to minimize on those US$1.x/minute Internet access fees.