Here's what I've learned from a recent interior replacement for my MGA.
Spray on adhesive worked much better than brush on contact cement for both carpet and vinyl trim. I used the cheapest stuff for the where low adhesion worked fine and better grades for high use places. Buy at Lowes / Home Depot.
For the gluing the vinyl to the door and cockpit rails, I used spray on adhesive along with gelled super glue for those places that needed to be held quickly. The gelled superglue was a key. No staples needed and I could not get them to go into the old hardened wood anyhow. Getting the vinyl smooth on all parts of the rail curves is exceptionally difficult and I never mastered the technique - just good enough was what I ended with. I don't know how the factory did it unless it was shrunk on. Keep the old vinyl when you remove it and use for a pattern, but cut generously.
Installing the lift-the-dot fasteners for the carpet was easier than expected. I sharpened one end of a 1/4 inch pipe nipple and put in in a drill to cut the holes - also used a 3/8 pipe nipple similarly for larger holes but had to weld a stub on it to get it into the drill chuck.
For carpet padding and sound and heat insulation I ended up buying thin duct insulation from Lowes/Home Depot in a roll - like bubble wrap with aluminum foil on each side. The spray adhesive worked very well with this, it was easy to cut and fit, and the carpet in turn was easlily spray adhesive-d on to the insulation - I'd definitely do it this way again, leaving out the padding included in the kit.
Seats are next.