Well, since no expert has weighed in, I’ll try. I’m just an Outlook user though, so take what I say with a grain of salt. My advice is worth what you’re paying for it. That said,
Get your new machine and just install Office (or whatever Microsoft sells that includes Outlook). Outlook stores all your emails, contacts, and such in a folder with a PST suffix. You should be able to copy your current PST file to a removable drive of some kind. Then you should be able to use the new Outlook on your new machine to “recover” or “restore” from your old PST copy. There’s a recovery facility built into Outlook, somewhere I’m too lazy to look for right now. That should get your whole body of data into your new hardware/software.
For backups, Outlook also has its own built-in system. But I use a freeware program called Safe PST Backup. And I use Dropbox. Set up Safe PST Backup to send a backup into your Dropbox. You can set it to do this multiple times a day if you wish. It runs in the background and does not interfere with the operation of Outlook. Then you always have a current backup “on the cloud” in your Dropbox. Anything happens to your Outlook, you can always restore from the backup. I work with Outlook all day myself, and I have backups sent at 10am, 1pm and 5pm.
Of course, to be really safe, you may want to also copy a backup onto some other safe place, like that removable drive. Do this every week and, no matter what happens, you will not lose more than one week’s work. Annoying, even costly, but not fatal. And this will (or should) only be necessary if Outlook corrupts your files without you noticing, and those corrupted files get sent to Dropbox. Incidentally, that’s one reason my first backup isn’t sent until 10am. That gives me time to notice if anything wonky has happened to my Outlook files, before they get sent out to over-write last night’s 5pm copy.
I think there’s a pay-version of the backup utility that gives you additional options, like multiple destinations, if you think that to be necessary.
ETA – you can of course use Dropbox and Safe PST Backup right now, on your old machine. When you get your new one set up you’ll be able to “restore” directly from the PST file in your Dropbox.