this is probably a better question for r/gameaudio , but I can help you. realistically, audio recording is a whole skill in itself that depends more on time spent doing the work rather than the specific tools involved. But to answer your question about a microphone - if you don't already own recording gear I'd recommend a does-it-all device like the Zoom H4N. it's portable for one, so you can use it in a dedicated space or take it around. That's important because a lot of sounds you want to record won't be right next to your computer all the time. It has 2 inbuilt microphones so you can record in stereo, and also doubles as a storage device and audio interface that connects to a computer (so you can use it to record directly into a Digital Audio Workstation program like Reaper or Audacity etc). you can also plug any other microphone into it and record using that instead.
Zoom H4N is pretty standard as an entry level recording tool, but plenty of pros use them in indie game audio. they're a workhorse and you'll be able to develop your skills using one for sure.
that said, a lot of times you might want to use sounds you can't go and record yourself. for example a wolf howling, or like elephants or something. just as an example. for that the freesound.com database is really useful - lots of creative commons (free use) sounds in there, that either require credit to the maker or no credit. I know that the popular game Donut County used a lot of freesound.com audio in the game.
re: your question on hyper cardioid: that's a directional pickup type (hypercardioid can be good for recording foley because the audio tends to be more focused at the front of the microphone, so other sounds are somewhat rejected). condenser microphones are best for foley but you'll do okay with something that's regular cardioid. something like a Rode NT1 is great for that, but there are loads of cheap large/small diaphragm cardioid condensers out there. either large or small diaphragm is pretty much fine for foley.
what I'd say is if you grab the zoom H4N, record your foley in MONO to begin with and not stereo. makes things much easier. Stereo is generally more useful for things like ambience and other sounds when you're starting out.
it's a rabbit hole, so know what you're getting into! but have fun and good luck :)