I highly recommend FastMail for a paid email provider. Their support staff is quick to respond, and it’s nice to be a customer instead of a product (i.e. pay for the service instead of getting it for free with ads)
FastMail have been an excellent email provider, and support has always been responsive and useful.
If you can, definitely try to run your own mail server for the experience but start of gradually, e.g. relay outbound email through an smtp service, and slowly add the different layers such as spam analysis, filtering, etc.
There are /so/ many layers to email these days that if you try to do it all at once you'll spend way too much time on just keeping the wheels from turning.