About your intro and outro
There are more ways of opening and closing your 'cast than you can shake a stick at. You can spend hours researching them. The one clear rule is that there is no rule.
So, let's go back to basics : decide what purpose your 'cast is to serve.
What purpose, that is, beyond building your brand - and, as it turns out, that's a vitally important, indeed it's an integral, aspect of 'casting.
One useful source for working out how you'd like the beginning of your 'cast to sound is radio. Listen to a wide range of radio programmes for a wide range of interests - and from a wide range of countries.
Intros have developed a lot in the past 25 years as producers, who live and (professionally) die by the numbers of listeners, have had to come to terms with listeners who know the value of their time and aren't prepared to sit around for ten, fifteen minutes or half-an-hour, for example waiting to see what comes next.
After all, you are delivering information not a murder mystery.
This is, actually, one of the reasons why I don't like e.g. instructional videos. I have to go at the pace of the video when, if it was in a page, I can read at my pace. That usually means five minutes instead of twenty, for example, and I can scan it first to see if it does what I need before committing even that five minutes.
So you are trying to capture that impatient person to persuade him that it's worth continuing to listen.
The intro serves several purposes: it warms the audience to your voice and tone so they aren't taken by surprise when you launch into the content; it reminds previous listeners that they have heard you before; it is your "calling card" for the 'cast, informing them of the topics and, even, including a few words of introduction. These words can be the same or an extract from the teaser you upload with your 'cast and which is shown on the "all 'casts" page.
It is obvious, then, that you need to put some thought and preparation into your intro.
I have a little script that is the same for each 'cast, followed by a short mention of content. You can find whatever you are comfortable with.
Also, I have music to start with, even before I speak and a "zing" that separates the intro from the main content. I have edited mine from a piece at music-for-video.com (note the hyphens - without them is the wrong site) using Audacity. We're in good company using that source: once you get to identify some of the pieces, you'll hear them on many tv and radio programmes from all over the world including, we're pretty sure, Formula One's in-house productions and several Chinese dramas. There are many other sources for free or single payment music that is suitable.
The outro is just as important as the intro although for different reasons.
While we are on the subject of music, I'll deal with that first. Again, this is what I do and you will have your own ideas or find inspiration elsewhere. For the intro, I use the first few seconds of a piece, for the "zing" I found a snippet to extract and for the outro I use a few second from near the end of the piece and faded it out before the actual end because it's clear that it's winding down by that point.
What's in the outro?
Three things. The first is the payload. This is the marketing message. It is short and to the point. You've got the listener's attention so why lose it by being very obvious? Next, remind the listener that they can thank you for your work through HonourPay. If you wish, remind listeners that they can subscribe to your 'casts. Remind that there are links to both in the 'cast page. And thank the listener for listening, say something nice. Again, I have a little script. Mine encourages the listener to come back.
I don't use the outro to reinforce the content. That's part of the content plan which is like an essay plan (see About writing your script for more on that topic.
Some light relief
Because we all deserve some light relief, here's The Intro and the Outro by the Bonzo Dog DooDah Band, the late Viv Stanshall. You might have to listen to it many times to work out all of the jokes and some of them are curiously English. I hope it makes you smile: https://youtu.be/yCtkJxyYsrc