Soundproofing is not simple but also not hard.
You can add mass to anything that resonates to dampen vibration. You can also use absorptive materials to break up sound frequencies. Dynamat is a mass loading self-adhesive product sold at car parts distributors and mobile sound installer shops. Fiberglass is a good absorptive material to use in enclosures and it's also non-combustible. It is made in compressed sheets for HVAC and spun variety for cavity insulation. Sold at building supply distributors and your local big box stores.
Good luck with the furnace.
