CD's were around in 1982, just not readily available and on the market. CD technology originated in the 70's! Heck, the concept of reducing sound to mathematical equations/numbers dates back almost 200 years (Nyquist)!
And as far as music equipment goes... newer doesn't mean better, nor does older... the two important factors for if something sounds good is APPLICATION and SOLID DESIGN. Better designed equipment sounds good regardless of if it is analog, tube, solid state, digital or software. The media is *NOT* the message... the music is.
That being said, picking the right gear for its sound depends heavily on the application. A metal band will sound better on some types of gear than other types of music might, or a particular use. The wise engineer knows how and when to choose what equipment for their purposes based on what is available.
And in my opinion, metal sounds best on an ANALOG setup. If you have the time and budget to do so you should track to analog tape through the best analog mixer using high end solid state analog equipment (tubes are IMHO too flubby for many applications in this genre). If I were to build a ultra high end studio it would definately include a 2" analog tape machine in addition to high end digital DAW's like the IZ Radar. However, my clients need to work fast and on low budget so I am mostly digital now and will be 100% digital within a year.
Honestly, once you've taken care of finding a place to record--which I recommend a studio if you want even "Kill Em All" levels of quality--the most important factor for having that raw 80's early thrash metal sound really is in YOUR hands.
The following assumes you really, really want that sound copied:
Obviously if you have a Mesa/Boogie Triple Rectifier you're not going to get that early Metallica vibe going on. You need a Marshall JCM800 and a Marshall 4x12 loaded with 25 or 30 watt Celestions. You need to have an Ibanez Tube Screamer running in your chain as well, because *THAT* was their sound. You also should think very heavily about
Gibson Flying V's because that was their main axe at that time period and they do have their own sound!
In general avoid the scooped sound. They weren't really doing it at that time. Instead, there are a LOT of scratchy, shitty mids on the guitar for that album. Make sure to copy their bad tone exactly!
Avoid mid to late 80's devices like active guitar pickups. That sound didn't pop up into their repertoire big time until "...And Justice for All". In fact, avoid anything overly fancy as far as time/modulation effects go. "Kill Em All" is a very, very straight album as far as production goes. No fancy reverbs, no fancy this and that... just the sound of the band.
I'm not sure how many overdubs they did guitar-wise for rhythm but I'm guessing 3. It's hard to say if KEM was recorded on a 16 or 24 track machine. Whatever it was I doubt if it was state of the art or extremely high end for the time. Definately not an 8 track though.
As far as drums go, having a double kick setup is probably a must, as are a lot of cymbals like Lars tends to have. To me the room sounded pretty 'live' and pretty big... so if you want that sound you should do the same.
Definately push the high end with EQ on the cymbals. That super pingy, washy, cymbal was definately the product of some serious EQ... possibly Pultec or other tube eq?
DO NOT... I REPEAT DO NOT attempt to get the overly dense sound of today. That immediately will kill your attempt to nail this sound. Pull up KEM on a wave editor and see how the full waveform is represented without serious limiting. If you want that punch on the snare you need to avoid the 'louder is better' cliche of now.
Good luck on your endeavor. I'm not sure why you want to sound like that but hey, that's your decision.