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The IRS adapter kit costs $395 plus shipping... but what is the total cost of all components to do the job?
Right, the adapter kit from Team321 LLC costs $395
The IRS from your favorite wrecking yard costs anywhere from $100 - $300
The required shocks are described HERE  and you will be providing the 1/2" nuts and bolts for the shock mounts.

What type of components will I need for a "complete" installation? Please list the sources and prices of the components and options...

The adapter kit from Team321 LLC costs $395 plus shipping. UPS shipping is between $25 and $65 in the continental US. I will need your complete shipping address to determine UPS pricing.  Alternately, US Postal flat rate shipping is $30 in the continental US.

The price of shocks range from $35 - $100 / pair

Shock mounting hardware :
    Upper shock mounts ( provided with the adapter kit $0 )
    Upper shock mount sleeve ( provided with the adapter kit $0 )
    Lower shock mount sleeve ( provided with the adapter kit $0 )

The factory coil springs may be used - but they may need to be cut. Remove between 1/2 and 1 1/2 coils - depending on desired ride height.
 I have seen Thunderbird Lowering springs or progressive springs listed on RockAuto.com, but I have no direct experience with them.

If using a Lincoln Mark VIII IRS, I recommend replacing the factory airbags with either aftermarket airbags or coil springs. There are a number of companies offering replacement coil springs - one is Suncore Industries.

Air Springs
Air springs are available from a number of sources. The good news is that all vendors follow a uniform mounting strategy, so a wide variety will work with these IRS adapters. The cost of these air springs range from $50 - $100      
I recommend  AirLift Performance 2500 airbags. Click this link for pricing and specs:

Airbag Pedestal Mounts

The airbag pedestal mounts I provide are designed around AirLift Dominator 2500 airbags and fit either the Lincoln or Thunderbird style lower control arms. The Lincoln Mark VIII Lower Control Arms are slightly different from the Thunderbird & Cougar Lower control arms. The function of the pedestal mounts is the same, but the design differs slightly.
I am not supplying the airbags, just the mounts. I am recommending Thorbros.com since they have been very helpful to me in the past and they provide quality parts and service. 
The cost of the airbag pedestal mounts is $145 per pair. Details may be found by clicking HERE to view the Air Bag Installation