Lizard Skin and Dynamat
 

I am a newbie to the rx-7 world and I am trying to do a top to bottom FC rx-7 build on my 1986 gxl. I ripped out the interior and removed all the sound deadening, and I am torn between the use of dynamat and lizard skin for a sound deadener. Should I use both if I can get my hands on them? or should I use one or the other?

How much quieter are you trying to go? I've done over a dozen cars myself with varying techniques and here's what works best:

Spray in Ceramic/Insulation - Hytech SC#1000 for Interior, Metal Shield #1267 for Exterior or Second Skin Audio Spectrum
Butyl Sound Deadener - Second Skin Audio Damplifier Pro or Noico 80mil Sound Deadening
Mass Loaded Vinyl - Second Skin Audio Luxury Liner Pro

Fabric Tape Everywhere... No more vibration noises.

You want to use BOTH of the products you're talking about for the best effect. It's absolutely worth the effort.

I want to be able to install a high end sound system and so that when I use it the metal in the car doesn't rattle or shake causing the subwoofers to become annoying to use. Also is there any big difference between noico and dynamat? I would rather take the cheaper approach, but if dynamat is superior then I will end up going with that option.

Noico is cheaper and superior than Dynamat. If you want the best, go with Second Skin Damplifier Pro.

Liquid Sprays like what I said are going to be absolutely the best option for you. The best option is to STACK all of it.