I also recommend an indexer like notmuch or mu to gain Gmail-like search and agenda capabilities.
Some quick googling[1] makes it look like you indeed do that first thing, and then set up a hook to load a different configuration file when you enter the folder for a different mailbox.
[1]: https://www.df7cb.de/blog/2010/Using_multiple_IMAP_accounts_...
Unless you actually need to do things like move entire e-mail threads between accounts, it works well enough.
While I like command line apps, and am a die hard vim user, there are just some applications that I really want to use a mouse for, and email is one of them. I've tried mutt a few times before and it's just never clicked with me. It's not that I can't learn how to drive it --- it's that I don't want to have to. Finding little-used commands is so much easier if there's an actual menu.
The little-used commands can be found by pressing "?" in any mode. You get a nice list including any custom macros you've set up (I don't use many, but a few are essential). It's far simpler than clicking all over menus and dropdowns and hovering inscrutable icons...
- FAST. Mutt lets you process thousands of messages in short order. Mutt is directly responsible for helping me dig out of a 50k deep email hole brought on by years of GMail's approach (archive, never delete) in a few days of on-and-off cleanup.
- Plays well with others. Uses a bog standard Maildir format that anything sane can read (including Thunderbird, so migration should be easy), provides a very powerful hooking system which can do anything from verifying PGP signatures to checking your spelling before sending to displaying attachments.
- Sane defaults. Doesn't require a lot of in-depth customization to provide the basics, and the bells and whistles are hardly out of reach.
- You have a backup of your mail for free (by using OfflineIMAP)
- Not hard to learn (at least for the crowd here). If you can use Vim, you can be using Mutt at full speed in less than a week.
- Search capabilities that blow nearly every other project out of the water (regexes with some very cool niceties)[1]
- Secure by design. Mails are rendered as plaintext, HTML is decoded by piping messages through a program like w3m. Tracking bugs can't do their job, spammers can't see that you've looked at their stuff, and you're immune to whatever image decoding bugs crop up. (Though you can still view images, it's an explicit process). Also, builtin GPG support.
I followed Steve Losh's guide[2] on setting it up.
[1]: http://www.mutt.org/doc/manual/manual-4.html
[2]: http://stevelosh.com/blog/2012/10/the-homely-mutt/