Before we talk about hosting, may I suggest you record your podcasts in WAV file format as it tends to be the best format to edit with. The files tend to be larger but contain far more data.
I tend to find an hour in WAV can be over 1 gigabytes in size.
You can then export the file to such as mp3 file format once you have edited the file.
To host, one option is free. This is the Anchor site and app. Both the website and app offer lots of options. Some podcasters say to avoid this site as they do not like the terms and conditions. However, I see no reason not to use this site.
But treat it like all free sites such as YouTube. Remember at any time they can close your account.
I use Anchor and so far had no problems using it.
If you plan to do podcasting properly and regularly then in truth you should opt for a pay host as this way you have more control and they offer lots of useful options, such as stats and automatic posting your podcast to other sites.
The site I use is libsyn.com. It offers a great deal. It provides great stats and is easy to use.
These sites will provide you with an RSS feed to add your podcast to other sites. The more sites and apps you add your podcast to, the more listeners you will get.