Hi David, @DavidF
Mail-in-a-Box uses Roundcube webmail. Roundcube has sieve filtering built in, so no need to get your hands dirty. 
MiaB would work well for your purpose I think. Though it would not be the recommended method, you can create a catch-all account for your domain, and then have those emails filtered and forwarded to the accounts you reallly want them to be in … or even to different folders within the same email account.
The recommended method would be to have mailboxes for cooking@ and basketweaving@ and astronomy@ to which your various senders would send directly based on purpose … but yes, the other way will work as well.
I feel for you being on Bluehost … they are an EIG owned hosting company, so yes … run! fast! get away from that horrible service.
Mail-in-a-Box is usually rather easy to set up, though sometimes things happen. But the community here can help you sort through any issues, often in real-time if you visit our Slack channel.
And if you really don’t want to run your own mail server, but feel that you have no choice to do so … I can recommend you to a good solid service that will do everything you want and more. For probably less than you are paying for Bluehost, and about, or not much more than you’ll pay for the VPS.