If you send an email on your phone, a copy of it is there waiting for you in your Outlook’s Sent Mail folder automatically when you are back in the office. And vice versa. No more cc'ing yourself in.
If you delete an email on your mobile device it's deleted on the laptop. So you don't delete it 2 or more times, like with a disconnected ordinary mailbox.
No plugging your phone into your computer to synchronise your contacts and calendar. All the data is synchronised, up-to-date and organised for you via the Exchange service wirelessly.
That can be achieved using any IMAP account, you don't even need a remote mail service.
So that's available with any decent hosting package.
All devices will sync.
As for calendar and contact functionality, it depends on whether you want to do this all through Outlook.
If you don't already, it's arguably easier through Google or other services.
Google's calendar lets you do all that, and works better with most people's phones.
Google doesn't integrate as seamlessly with Outlook as Exchange, but Outlook is arguably a terrible email client and piece of software.
We normally recommend Thunderbird.
As for the the out of office point, that just highlights a ridiculous problem with how people used Outlook.
You can set your out of office in Google Apps Mail, or your hosting webmail interface if you're using your hosting account's email service.
Also if you want to use Exchange, you can just get it through an Office 365 package direct from MS, which is Microsoft's answer to Google Apps for Work.
This will likely provide much better value for money.
I'm regularly surprised by the lack of awareness of IMAP. We recently migrated a client that was only using POP3, who thought they needed Exchange so their email would sync on their phone and laptop, and so they'd have access to archived emails in folders.
IMAP provided all the functionality they required without the additional expense.