I don't know if anyone has posted info like this before. But I learned this and it was very helpful to me for weapon/acc upgrades.
You can raise your multiplier easily by buying 36 of the 80 gil items in the creature shop. Things like Sturdy Bone, Barbed Tail and Vibrant Ooze. To get to the 3x multiplier the most effectively, use them in this order. 4 > 4 > 7 > 3 > 18. Now if you have plenty of money and don't care about the most effective way to use low exp items, then just throw all 36 on at once and it will jump you straight to 3x multiplier.
There are different symbols for organic type items and man made. Basically things like bones, tails, etc are used specifically for boosting the upgrade multiplier, and the man made things like metals are used AFTER you have a 3x multiplier. Don't waste your good materials before having a 3x, it's not hard to get.
I believe the best exp for your money are turbojets, which you can find in the garage shop. So once you have a x3 buy a good amount of these and use them on that item. There are things that give much more exp in a single item, but that doesn't necessarily mean it's better gil/exp. And of course you will find good items during the story line and from missions as well. When you do use the big exp items, they will give you full exp for however many you used, but it will decrease your multiplier. So what i do when that happens is use organic items two at a time until it's at x3 again, just to use them most efficiently.
Basically for an idea of what each upgrade costs, it's from lvl 1 to cap is 50,000 exp, intermediate to cap is 450,000 exp, and ultimate weapons are 1,500,000 exp to cap.
The best EXP giving components are: (all EXP boosts are averages)
Ultracompact Reactor - EXP 40,000, Buy Price 50,000
Particle Accelerator - EXP 4,800, Buy Price 10,000
Tesla Turbine - EXP 823, Buy Price 1,800
Super Charger - EXP 774, Buy Price 1,600
Turbojet - EXP 768, Buy Price 1,600
To sum it all up:
1.) Choose an weapon / accessory to upgrade.
2.) Use 36 sturdy Bones, barbed Tails or vibrant ooze to get a x3 multiplier.
3.) Use your turbojets or other metal materials for a big exp jump.
4.) Use your sturdy bones again (I do 2 at a time) to get back to x3, unless it dropped all the way down, in that case 4 > 4 > 7 > 3 > 18 order.
5.) Use transforming items to upgrade the item.
6.) Rinse and repeat until you're finished.
You can level every weapon in the game to 2nd tier cap, and then choose the one you like best to fully upgrade to omega weapon (that's what lightnings is called anyway). So don't worry if you think you are leveling a less effective weapon.