8v lumps are bomb proof, so good call on that, also you are very sensible to go for weight reduction as your first mod. it is probably the single most effective modification you can do on a mk3 as it is a bit lardy....
if it were me, this is what id do....
1. lower the car on some good quality shocks and springs. think koni,apex, avo etc and you wont go far wrong.A Good quality shock and spring combo will ALWAYS provide better handling out the box than coilovers, which need to be counter weighted and set up with precision to be as effective)
2. Give it a diet. remove rear seats, all trim, passenger half of the dash (can be made to look good with some fibreglass and skill) passenger seat (no passengers wouldnt bother me!) remove all excess metal, inner door skins, chop into body with holesaw under bumpers, remove all sound deadening/ tar (this is generally 10kgs on its own!) etc etc etc
3. upgrade the brakes, vr6 items if you have a 5 stud or g60 mk2 items if you have 4 stud. larger master cylinder also helps. think you can go all the way up to a 26mm item from some SEAT's and possibly a later Passat??you should have a 9" servo as standard i think, if not, id fit one. also fit braided brake lines all round, and completely drain the brake fluid system, flush, and refill with dot 5.1 fluid.
4. engine mods, 276 cam and vernier pulley, k&n panel filter in Original airbox, ported and polished head with bigger ex valves, blueprinted (pistons,flywheel,crank etc lightened and balanced), 4-2-1 manifold and full 2.25" stainless exhaust (larger bore due to other mods, stick with a 2" if not doing headwork/blueprinting) then a remap to make most of all the extra flow the engine now has.
and yes id do it in that order. it is much more cost effective to make your car faster point to point than it is in a straight line. with better handling you can corner faster, better brakes means you can stay on the throttle that bit longer etc.
THEN go nuts on the engine!
carbon is all well and good, but is very expensive for what it is, you can replace a boot,bonnet and wings in fibreglass for the price of a decent bonnet in carbon. Polycarb windows are also a massive weight saving that often gets overlooked.
hope some of that is useful for you!