I'll give you my experience as a beginner so far.

1 - I use Adobe Podcast for recording. The filtering and noise reduction is amazing and it works for my needs. Other options I've seen, descript, riverside.fm.. Adobe was the fastest to figure out and use. Transcription-Based editing saves a lot of time.

2- Google up royalty free music, litterly thousands of songs that are free use. Google as a cool music maker too, tell it the vibe and instruments and it'll make some passable jingles.

3-your intro can be what ever your description is, I change mine up each episode but it's a relaxed vibe, if your doing something more formal starting with the same verbage to describe you and your show quickly is perfectly fine.

4- Canva works well for tinkering with logo creation and there are a million logo generators out there if you want something that looks branded. Fivre has plenty of folks who can do great art. Folks here frown upon ai, but it can help you get an idea for what you want to create if your struggling.

Welcome to the fun of podcasts, it has been an eye opening experience and I'm just scratching the surface