The trend these days is for online mail, which is great for access but a bit shoot for long term storage. I have always used a POP email address as my main email, normally one from my ISP, though again, not all offer it now. POP delivers your mail locally which has the advantage of you being in charge of storing it and archiving it but the disadvantage of it only being on one device. I use online mail, such as gmail for throwaway stuff, shopping, newsletters and other unimportant crap. I configure my pop mail to remain on the server for a few days, so that I can use a third party android client to retrieve it away from my home PC. If I receive anything I need to access remotely i.e. a hotel booking or similiar, I simply transfer it to my gmail.
So my setup is: ISP provided POP mail sitting on a client on my PC, Thunderbird, and online mail, Gmail, which I can also configure Thunderbird to handle on my PC. On my phone I have access to gmail and use bluemail to pull down my ISP mail. On my PC, Thunderbird is backed up to my SAN and also online via MOZY.
Have you got all that Pubby or should I start again?