Also check out EposVox channel and Gaming Careers.
And look into these audio interfaces, especially USED:
PreSonus or Scarlett or Behringer. Those can be had starting at $50. And used ones will work just as well, check on Ebay. Then pair it with an XLR condenser mic, which you can get as low as $20. There are a lot of condenser mic clones from China on Amazon and Newegg that come with the whole kit: mount, pop filter and arm. The brands above also sell whole kits, but seem a bit expensive. You can always upgrade piece by piece later if your channel gets larger. The USB audio interface will work with many mics.
You should try searching for other posts in this sub that ask the same questions. I'll just paste my answer from another post:
You can go cheaper on the mic itself, if you pair it with a decent USB audio interface, like PreSonus or Scarlett or Behringer. Those can be had starting at $50. And used ones will work just as well, check Ebay. Then pair it with an XLR condenser mic, which you can get as low as $20. There are a lot of condenser mic clones from China on Amazon and Newegg that come with the whole kit: mount, pop filter and arm. You can always upgrade piece by piece later if your channel gets larger.
Then use OBS Studio and the built-in audio filters to cancel out noise and gain to boost it. And you'll be able to upgrade pieces as your needs increase. I recently got a better mic arm for my setup, but keep using the same mic and USB interface.
I think a lot of people get frustrated with the pure USB mics, which are either too sensitive to noise, pick up the electrical interference from the PC, or don't have enough gain.
Also, check out YouTube channels that talk about streaming or recording games. They review a lot of equipment and help you with good setups.
Here are some recommendations:
Gaming Careers channel:
https://www.youtube.com/channel/UClx4eJ_EP9MJdz19JUjKD1w/
Epos Vox channel:
https://www.youtube.com/channel/UCRBHiacaQb5S70pljtJYB2g
Epos Vox's OBS Master Class:
https://www.youtube.com/playlist?list=PLzo7l8HTJNK-IKzM_zDicTd2u20Ab2pAl
Here is a reasonably priced mic kit from Neewer:
Condenser Mic kit, with Phantom Power, arm and cables:
https://smile.amazon.com/Neewer-Professional-Condenser-Microphone-Suspension/dp/B01D4KYRYC/
Lastly, you will want to use your capture card to get video from your PS4 and capture it with OB on your PC. At the same time, you will capture your mic audio in OBS, to output a video file that will have both the video and audio together. The YT links above talk about how to mix different sources in OBS.
BEHRINGER U-PHORIA UMC22 https://www.amazon.com/dp/B00FFIGZF6/ref=cm_sw_r_cp_apa_R1cCzb3TSGV7N
This is what you want instead
It's a very central part of every studio setup, it essentially does the processing on the sound (taking the load off of your computer and providing better sound quality) and provides I/O for connecting XLR mix, 1/4" jacks for guitars/synths etc. and balanced outputs for your monitors if you choose to get them. You will definitely need one before you get monitors, and I recommend one regardless. It'll smooth out the frequencies in the sound and allow you to hear inconsistencies better on either headphones or monitors.
This is a step down from the one I use, but the only difference is this one has one less XLR input, which I doubt you need. Behringer is budget friendly and makes great products in my opinion.
Let me know if you have any other questions.
I'm not familiar with the PS4 and what inputs it has, but I would recommend a USB interface to run your mic through. It will allow for the best quality audio on your PC, but unfortunately I don't know much about the PS4 so you would need to look up to see if it would work for that. If your budget allows, you could always get a Zoom portable interface/recorder as it can run through USB to your computer and through a "line out" (standard 3.5mm audio jack) to the PS4. You may also be able to use a mixer for the same purpose, but look into what you need/have the budget for before you buy.
The products I linked are just starting points to help you out, but should fill your needs if you decide to go with one of them. Good luck, and I hope you can get everything running smoothly!