- I wouldn't go with a Yeti (which, despite all the idiotic memes around it, is fine for a starting microphone). A condenser mic is generally going to be more touchy and more susceptible to room noise issues, which you'd probably rather avoid. Instead I'd go with something like the AT2005USB; its DAC is fine and it provides an XLR output as well (and you can use both, which I do for some tasks such as voice comms in games plus routing audio to my mixer). Knox also makes a good knockoff with similar characteristics.
- Audition is a good call, especially at $20/month, but IMO (and this is all totally subjective, don't take my word for it) Logic Pro X is my jam. However, these days, live-shows-to-podcast seem to really taking off, particularly on Twitch; to that end, you're probably going to be mixing in either OBS/Xsplit/vMix (eww) or mixing in your audio app and routing to the video compositor, so be ready for that.
- Zencaster, Skype Call Recording, etc. are all fine, but they all have one really big drawback: they're most useful for offline shows. The work required for Skype/VOIP guests in online shows, unless you're happy letting Skype mix the voices for you (and you shouldn't), is nontrivial. I'd try very, very hard to stick with in-person podcasts with local people until you can really hack it, because VOIP'd casts are noticeable and often have a big hit to both flow and to audio quality.
 - https://www.amazon.com/Audio-Technica-AT2005USB-Cardioid-Dyn...
 - https://www.amazon.com/Knox-Gear-Cardioid-USB-Microphone/dp/...
It handles all the audio routing for 3-way (or more), and recording too if you want it. VOIP interviews can be unnoticable -- in practice you have probably heard remote interviews on the radio done with systems like this, and may not have even realised it.
I've looked at Cleanfeed and it looks like a really cool beta product, but it doesn't feel like the product appreciates how existing audio stacks and production flows work. And that's not entirely Cleanfeed's fault, because there are browser limitations, but at the same time the browser is not a good audio production platform (only Chrome seems to recognize the existence of multi-track audio devices, and that seems to be more of a "here's a 5.1 surround sound system") and that's a problem too. Like: I run a US-16x08 locally. It has eight mikes and eight line-ins. Cleanfeed (and this is probably Chrome) gets confused and says there's no microphone unless I go into Chrome's settings and force-pick the US-16x08, and then it just gives you mic one? It's mixing down the remote, too, so I just get back a single audio stream. This isn't acceptable; I 100% need to feed this into my mixer, not just splat out the audio. If I just wanted to mix down, Discord provides acceptable-not-great audio quality (and it appears there's probably a way, if one is a wizard, to rip audio streams out of it separately and push them through something like Soundflower).
If Cleanfeed was a local server that connected to you guys and had VSTs I could drop on instrument tracks in Logic to get individual voices out, I would pay you nontrivial money for that.
Also, video is pretty important. If Cleanfeed supported video at a size/quality that I could cap it out of a browser window I'd probably pay for it despite having to rework everything else; that would be a killer-app feature to compete with vMix Call.
Feel free to ping me offline if you'd like to chat--my email is in my profile. I think Cleanfeed has potential and I'd be happy to talk about this more in-depth.
And no mention of headphones or speakers for yourself either..
Which then ties into the A/D converters which were earlier dismissed as superfluous..
My bet is that even if the mic is not quite as good, something like the focusrite scarlett solo studio pack (~199 - comparable to the 'pro' mic cited) will net overall better results since you get a full loop of prosumer/pro grade audio rather than just the input side covered.. not to dismiss the high importance of a good source track..
don't know this kit though; check sound on sound and soforth if someone is serious. I do have focusrite USB IF and it sounds great.
 - http://www.clearone.com/products_beamforming_mic_array
 - https://www.youtube.com/watch?v=PjVmMvmQFOM
Professionals will do basically the same thing, only upgrading the mics to ElectroVoices or something.
Maybe you want to, or have to, record audio outdoors.
Maybe you need to record somewhere where construction or work is happening in a single direction.
Does anyone else have other recommendations for my use case?
1. made a good choice for the everything you need
2. went ahead and picked a solid choice.
For someone starting out, it would be better to just make these choices than have to suffer the tyranny of the paradox of choice.
I think we'll have to put together out list of varying equipment as we cast from very remote places.
As an audio professional for over 30 years I have one question for you. What is one thing that people will stop watching/listening before any other? Yup, it's bad sound. Google did some research on this in the beginning of youTube. People are more likely to stop a video with bad sound than bad video quality. So my recommendation is to spend some money on a decent mic and interface (ADC/DAC) than buying a usb microphone. So as I'm recently starting a podcast of my own I decided starting off I wanted an EV RE20. Standard radio mic for like 50 years or something. For a good reason, high quality sound and the proximity effect is minimal. Which is important when talking on a mic, saves time in post eq because of variable distances guests or you when speaking into the mic during an interview. Now not everyone has $499 to drop on a mic right? So they've also made a cheaper version for $260 called the EV-RE320. That sounds pretty freggin good. There's also the Shure SM7B for $399 which is a pretty damn good standard. Standards are there for a reason because that is literally what you're competing against and what your listeners are expecting. You can check out the comparisons on the web that helped me make a decision other than an erroneous article that seems to be way off base to me.
I have found Audition to be extremely limiting is how I would like a DAW workflow to operate. There are too many problems for me to take it seriously but I really don't have the time to go into at the moment. I would however recommend Reaper after using it for the past 3 years on and off. Although it may not have the prettiest UI it sure can do some amazing things with audio routing that kinda makes it ahead of the game in a lot of ways. I have spent many years in front of Protools and although I still have a soft spot for its ease of use, they kinda just started pricing themselves out of the market for me upgrading towards my needs as I'm not a professional studio engineer anymore.
So here's my suggestion within the author's cheap equipment budget of $369-439: Take the $240/yr you're going to spend on Audition and buy the EV-RE320 and Reaper. That leaves you with $40 towards your mixer (if you plan on having multiple guests in your studio) and audio interface which will cost you around another $200. Just my brief ideas of how to spend the money better and get a better sound. Now as far as the content well that's up to you!