If you don't want to compromise, expect to spend the next several months just learning about the process.
Set a budget now, watch some recording and mixing videos, read and watch reviews, and then re-evaluate your budget.
Do you have a decent space to record in? It's not just about volume, it's also about reflections. If the room is concrete and brick, you'll get lots of reflections that will muddy things up and suck. Consider budgeting going to some sort of studio to record drums, since these can be finicky and hard to get right in a bad room.
Don't bother with a bunch of reading; go hit up YouTube and watch how to do it. Listen to how different mics in different placements sound. A lot of this process is in your ears, not your eyes.
You want a computer that you're comfortable using. Are you a Windows person or a Mac person? Both are up to snuff for doing audio work. Windows machines are cheaper but generally, need to be replaced sooner. On the flipside, a Mac is a bigger investment upfront but lasts longer. I'm using a 2012 MacBook Pro that I bought used and upgraded the hard drive and RAM on. I just cannot get around the basics on a Windows computer. If you can, do it. Use it.
Lots of RAM is good: 16GB is the minimum I'm comfortable working with. This will allow you to have lots of processing going on without things slowing down.
A big hard-drive, preferably solid state because they are faster to read/write. Storage is cheap; I've got 1.25 TB solid state in my MBP. Do not start recording a single damn thing without having an external drive to backup your work to. If it doesn't exist in multiple places digitally, it doesn't exist anywhere.
Processing speed matters most for running virtual instruments. I can't imagine you'll be running virtual instruments and samples for a grunge project.
If you're gonna record a drum kit, you can use literally as many or as few mics as you want. For grunge, you can try using just three; two overheads and a kick mic. Or four; add a close mic for the snare.
Aim for mics that can serve double duty. SM57 and SM7B are great for snares, also good for loud vocals and guitar amps. A pair of small or large diaphragm mics are awesome for drum overheads, and can also be paired with the 57 or 7b on a guitar amp to get great tones. Don't buy a mic that has amazing reviews on vocals and poor reviews for drums or guitars if you're trying to work within a budget.
Since you'll be using multiple microphones, you need an audio interface that can support at least that many. Personally, I'd get something that you can add more inputs to via S/PDIF ports. An eight-channel interface would be great, then you can experiment with your drum miking plus allow you to plug a bass direct in so you can track bass scratch tracks with the drummer.
Software is tough; I'm invested in ProTools. Expensive. Seems daunting, but honestly, they're like big name supermarket brand foods; they're basically the same, they just have a different wrapper on them. Once you learn one DAW, you can transfer those skills, you'll just need to learn new button combos and keyboard shortcuts. I've never put any time into anything outside of ProTools and Logic. There are others that are cheaper, but I can't comment on usability.
You'll have some good headphones for tracking bass, drums, guitar, and vocals: closed-back so what goes into the headphones doesn't bleed out back into the mics. For mixing, get a set of open or semi-open headphones. Lots of threads all over the internet. People will yell at you and say don't mix in headphones. As long as you check your mix on multiple other listening systems, mix with headphones if you want.
Don't totally cheap out on mic stands and shock mounts. Some mics are fragile. Most cheap stands are light and flimsy with poor connectors and threading. Get some sandbags to put on the base of the mic stands to keep them in place. Also good for keeping a drum kit from sliding around on the floor.
Get a DI box for plugging your bass into.
Lots of XLR cables. 1/4" cables. Mic stands. Gaffers tape. Picks. Cough drops. Snacks. Coffee. Tea. Music stand. Power strip and extension cords. Paper. Pencils. Pens. A comfortable chair for the hours you'll be sitting down working on the mix. Tylenol or whatever you like to cancel out headaches. Patience. TIME. These are all things that you might not think about in budgeting for your project; but trust me, the little things really add up.
Don't try to involve anyone else in a project for exposure. My favourite response to requests to do work for exposure is "People die from exposure." Get others onboard because they are passionate about the project and want to do something fun, for fun, for free. Don't offer this as an opportunity for exposure and getting their name out there. Nobody takes free music seriously these days... you can sign up for Spotify or go on YouTube and hear the worlds biggest songs for absolutely free.