
Shure
SM58
Indestructible live workhorse; but muffled for studio vocals.

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Hi! For lightings, I think you can find a variety of cheap ones on Amazon or your local e-commerce website For Mic, if you have a tight budget, I recommend USB mics like: - Blue Snowball - HyperX solocast - Razer Seiren They’re plug and play and sounds so good. Everytime I speak my friends always surprised how good the quality is. It’s more than enough for beginner streaming/recordings If you have tighter budget, then I recommend Lavalier mics. Many options as well online Hope this helps!
If you are doing just basic stuff, get either Solocast X for $40 or other cheaper brands like Haono or Fifine. If you want to go DIY route and make a mic for cheap but sounds decent, get BM800 microphone for housing (or empty housing that is OPA Alice compatible) and use OPA Alice to build a condenser microphone (<$50 for internal parts). However, you will need minimum phantom power to power this mic.
I'd go for the Shure, because the SoloCasts sound conventionally good, but not for VO. And the Yeti is just pure garbolium. None of these will sound particularly "good", but if you don't wanna pay for an interface, the Shure will do somewhat do the work.
I would suggest hyperx solocast that’s what o have been using and it’s good
For something within the scope of your budget -- Simgot EM6L or Kefine Delci AE. If you are going to marry him in the future then get the Kiwi Ears Astral. According to reviews and this subReddit Top 5 Best for Gaming it is the best for gaming overall. For better audio pick up and less axis noise, get him an external mic (Hyper X Solo-Cast) that'll be plugged into his PC. Also a DAC too like the TRN Black Pearl among others to clean up audio signal from PC. 
Eu uso um hyperx , solo cast n tenho do que reclamar
Eu nem uso software kkk so pluguei e uso a anos

Shure
SM58
Indestructible live workhorse; but muffled for studio vocals.

Shure
SM57-LC
Versatile for instruments; needs pop filter for vocals.

DJI
Mic 2
Unbeatable convenience, 32-bit float; but poor Bluetooth audio.

Samson Technologies
Q2U USB/XLR Dynamic Microphone with Accessories
Great value dual USB/XLR; recent price increase noted.

Shure
SM7B Vocal Dynamic Microphone
Professional vocal sound; but expensive, needs external amplifier.