When you start a blog, you should also get yourself a separate email account that will be used only for the blogging system interface. (My experience is only with WordPress blogs.) Depending on how you adjust your Settings, you can receive quite a few emails from the WP system. It will be best, imho, that you keep these emails separated from your normal mail so you can respond as needed.
You can use any email system your prefer. You can get free emails from Google, Yahoo, Microsoft, and so forth. I went with Google and Gmail because I am used to it, and they have great filters.
Here are 3 Gmail filters that I really like because they help sort my blog’s control emails into 4 separate folders. #1 is for keeping a list of folks who have decided to Follow my blog. #2 is for people who Liked something on my blog. #3 is for mail that I send to myself for memory sake. #4 is everything else (such as Comments) that will stay in the Inbox.
This post is not meant to be a tutorial in Gmail. You need to create the labels before activating the filters, for example. And in #3 above, mymail is the name of your Gmail account.
On my iPad I use the IOS mail system linked to my different mail accounts and can see if I have blog mail that requires immediate action in the overview scan. I can browse the special folders later at my leisure.
It works for me…