What insulation to add under the new metal roof on the existing roof?

while adding a furring strip [your 1x4] might be needed to properly secure the metal roofing, it won't add any insulating value.  [The air gap is too large]  however, you local building supply store has the insulation product you want ... tell then what you're doing.  they know the local climate [we don't] and will recommend a stiff 4x8 sheet product.  they'll also tell you if the metal roofing can go directly atop it or if you need something like some 3 ply plywood in between.  -- grampa

When you do insulation, you really need a "cavity" which you can fill with an insulator. If you don't have the space on the inside, then you would have to do it on the outside. You can fill your cavity with straw (the green craze), fiberglass roll, polystyrene beads or board etc. So first make the cavity with wood, add the insulator, seal it up, add the  vinyl sheet, then the metal roof.       

You have a lot of options, but as you already have your deck you ought to look at a warm roof construction of vapour control layer (you may be able to get away with the old membrane) rigid insulation board and your metal finish (or look at composite insulated metal systems which simplify things. You need to look at proprietary data for products in you part of the world, they give lots of different constructions for extremes.

Let me draw this simply .  You got a Box(garage) and on top of the box you got a triangle(roof).   You are ONLY INTERESTED IN KEEPING THE  temperature of the box livable. So insulation goes on the walls and flat ceiling of the box. Fluck the triangle.  You are not going up there.  If anything up there is cold storage. Many do not use that triangle for anything.  Nor is it strong enough to support your weight for long.
. So you want to insulate the box . That is the walls(if you got double plywood sheeting on it - outside and inside then you got to take off the inside layer of plywood and stuff insulation in between the wall uprights and put the inside sheet back on over it to protect the insulation.  As it is not a LIVING area, then there is no need for a vapor barrier(plastic) between the inside plywood and the uprights.(as there is no cooking or bathing or continuous living(so breathing) Heating is not continuous so evaporation is not continuous.  It is a workshop.
The box ceiling is also fitted with insulation, You may want the paperbacked type as you can staple the ears to the ceiling joists as most ceilings are not finished and just show open rafters and joists. So now the basic "box" is insulated.  The rafters stay open so the cool air will take away moisture still evaporating from the wood so there is no wood rot.
. Keep it simple and live with it.  It is a shop.  Tools don't care how hot or cold it gets.

U can't add insulation on the outside...lol