There are really three factors to consider when assessing possible podcasting solutions.
Podcasting reach by publishing to multiple podcasting directories
Reach is an issue in that the more platforms you post the audio to, the more avenues you are providing for people to "discover" the content.
There is a difference between just getting the regularly updated podcast episodes posted to your website and being available on all the podcast directory services. In addition to providing exposure, the directories provide the tools for your listeners to easily "subscribe" to the podcast without having a bunch of technical knowledge about how to connect to your website's audio RSS Feed. Here is an article listing the most popular Podcast directories.
Keep your podcast workflow as simple as possible
Workflow is a concern in that you want to be attentive to capturing high quality audio and providing good consistent production quality. You will want a good mic. I have a Blue Snowball that I love for its balance of price and high quality. In short, how do you get from recording high-quality audio to editing and posting that recording to your website and all the podcast platforms regularly and easily?
How to podcast on a budget
You can spend a lot on hardware, software, and distribution services. Fortunately almost all of that is unnecessary. Aside from getting a good microphone, everything else can be had for free. My best recommendation is a service called anchor.fm (https://anchor.fm). It is a service that is owned by Spotify which I believe is a "good thing" in that there is a major well-established company behind the service. You retain ownership and copyright of all your content. They reserve the right to use and distribute your work. Anchor provides a ton of information about how to get up and running in their FAQ. They also have a large blog with tons of podcasting topics. Anchor provides very easy tools for production, distribution, and analytics. If you go with their service they give you an easy to use embed code that allows us to pull that information back into your website.
You can do everything for free if you want. If you decide to monetize your content by using their optional ad service, they take a 4.5% cut of all ad revenue. Initially, I would not worry about getting wrapped up in any of this as your primary goal is likely exposure not ad revenue. Building an audience is a lot of hard work. You have to do that before ad revenue is even a possibility. It is just good to know the business model so that you understand why everything is "free". You can check the Anchor Terms of Service for all the latest updates to their model and pricing.
So, dive in. Check out https://anchor.fm. Let us know when you have things setup with a ready-to-go embed code and we can help you get that setup on your interGen hosted website for your podcast audience to enjoy with every episode you create.