Here is the manual way to set things up:
1) Set up your new email account. I recommend Gmail but there are lots of other free providers. I suggest using the free ones no-matter who you pay for service. This way you never have to switch again.
2) Import old email and information to the new service
3) Set up an auto reply in your old account to inform people of the switch
4) Update any banks, Facebook or other online service of your new address.
If you want an easier way to do some of this you can hire us (of course) or use Yippie Move to transfer all of your old email and contacts for only $15. You can see them at https://www.yippiemove.com/
There is going to be a bit of work, but, especially, if your old service is going away, it is much better to do it as soon as you can. That allows you the leisure to keep the old account for a while till you are sure everything is switched.