I've worked in podcasting for 12 years and have used a bunch of equipment in that time. These are my favorite products for a solid podcast including microphones, lighting, cables, and editing.
A solid microphone for streamers as it captures a lot of sound and has a very simple mute system. Great for podcasters as well, but make sure you have a silent environment otherwise it will pick up background noise
HyperX QuadCast Microphone
Silent and sturdy, which is exactly what you want in a mic stand.
Broadcast Booms
Hands down the easiest way to record and edit your show.
Riverside
Dynamic microphone that's perfect for podcasters and voice actors.
SM7B - Vocal Microphone
Do yourself a favor and get two 10' XLR cables. You may not need 10 feet of cable right now, but especially if you're starting out, your setup will likely change. It's worth having the extra cable length in the long run.
Cable Matters 2-Pack Premium XLR to XLR Cable
You don't need to spend hundreds of dollars on lighting. You want at least two lights on you and this does the trick. Once you get your space figured out, you may want more lighting. I use four, two on my face, one light above me, and one light behin...
Weilisi 10.2" Desk Ring Light with Stand
The easiest and cheapest way to add some sound deafening into your space. Put these on the wall opposite your background. If you can use a corner or closet, even better!
Moving Blankets - The Home Depot
Don't forget a pop filter! Especially if you're new to being on the mic, this will help eliminate those pops of sound from being captured. Again, this does not need to be expensive.
Aokeo Pro Microphone Pop Filter Shield for Blue
An easy way to adjust lighting or camera in an instant. Program the buttons as you see fit and just press one when you're ready. Very user friendly. While not a neccesary part of podcastin, it can be a very helpful tool.
Elgato: Stream Deck
If you're going to be on your keyboard while recording, you need to have a silent keyboard otherwise you'll be editing out clicks between sentences.
Silent Keyboard
By far the most luxury of items on this list but it does add a professional feeling to an at-home studio. Great way to let others in the house know to keep it down or not interrupt while you're recording.
On Air Light Sign
A 4k camera is essential for video podcasting. Recording in 4k makes your uploads in 1080p look phenomenal. Logitech is a staple in the industry and I use many of their products including webcams.
Logitech 4k Webcam : Electronics
This ring light works with Logitech webcams so you can record while being illuminated from the same direction. This light can get bright so adjust it to fit your space and comfort.
Webcam Ring Light for Logitech C920,C922x,C930e
Nothing hurts audio like the sound of a glass or mug clanging onto the desk. Hard coasters don't help so make sure you get a few felt coasters to dampen the sound of you glassware.
Felt Coasters For Drinks
Headphones! First, make sure you get wired headphones. Beyond that, they don't need to be expensive. I like these because they are inexpensive yet still look chic and cool.