Thunderbird Mail to Cloud Based Mail

[jwm2]

Ok well heres the scenario. I have an iMac (desktop) and a Macbook (mobile pc). I also have an iPad and iPhone. Right now I use Thunderbird on my iMac with multiple email accounts (probably about 10-12) and have multiple folders for which i keep certain emails (i.e. vendors, domains, etc). Now what i would like to do is be able to access these emails on more than one machine. What is the best route to do this? I would like to be able to sync emails between at least my laptop and desktop and if theres a good way to add the mobile devices that would be icing on the cake. I've checked all over google and have come up with numerous different ways of doing this, but which way is best? I like the look of thunderbird with the account and folders pane on the left and the email message list on the right and a preview under the email list. I have tried the mail.app but really don't care for how it looks. I tend to get hundreds of emails per day and would like someway of keeping things organized. Any thoughts on what I might do? Thanks in advance!