Specifically with Weapon upgrades. I'm just not getting it. Can someone offer a brief explaination what to do and how to approach it?

I get the basics of adding components but it's just knowing which to put to which weapon and also any new weapons I recieve seem to be way weaker than my current ones (my current ones haven't been leveled up) is there any point in caring about newer weapons?

One weapon isn't really weaker or stronger than another. The difference is mostly in how it affects your attributes and what characteristic it has (stagger lock, etc.) So depending on your play style, you may want to use a particular weapon.

For what it's worth, I never really upgraded anything until the post-game and never ran into any trouble by neglecting it.

Hmm, so far my crappy weapons are seeing me through as I'm more magic orientated than strength but we'll see how long that lasts.

Also is it my imagination or do the post-battle ratings don't mean/do anything?

Right the weapon upgrade:

As you said in the OP I assume you know the following:

Basically use all the animal stuff to increse the multiplier, then use the big XP giving mechanical items in order to give the weapon loads of XP.

After you upgrade levels of a weapon you will eventually reach a "star Level", after this you need a special item to upgrade it to a "tier 2" weapon. The final Tier weapon is a Tier 3 weapon.
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I stuck with Lightnings Gladius weapon

BUT really you want the weapon that suits the way your playing, I was using lightning as a commando more so Gladius was a good matched as its original affinity towards Strength was higher than magic.

Light's origninal weapon blaze Edge is more balanced apparently.

Then you get a weapon for Hope that adds a EXTRA +500 MAGIC when you level it up to a tier 2 weapon. No idea what the weapon is called though, sorry.

Right now I'd reccommend that you upgrade lightnings weapon & keep gladius on her if you wanna focus on light as a commando, even though I use her more as a ravager now.

They do, actually. Your TP will recharge a lot more quickly if you get five stars than if you get only four. It also improves the drop rate for spoils, I believe.

Having shitty level 1 weapons gives you a slightly higher target time, which can be especially helpful if you try to five star all the Cie'th stone missions.

Post battle ratings affect the number of CP you get & the amount of TP I believe.

use different monster parts to increase the bonus and then use metals to upgrade. you generally want to upgrade with a X3 bonus so upgrading goes quicker

EX: use 5 monster items- bonus x1.25, use 5 more - bonus x1.50 and keep going till you hit bonus x3

then use a metal such as "particle accelerator" and upgrade quickly

and the post battle ratings dont mean much. i believe the more stars you get the more TP you recover at the end of battle. not sure* but it might be related to item drop rates too.

oh yeah later on you get this weapon for lightning that fills up her ATB as you attack (only fills up the ATB really slowly each time you attack) so its a bit like haste on a minor scale.

But by then I had invested in my weapon got for lightning from the beginning of the game so I didn't use that weapon but apparently its really useful.

so you may actually want to wait till you get that weapon the weapons name isn't a spoiler but its a great feeling when you see its name, you'll know why so I won't spoil the weapons name for you.

Maybe you'd want to instead level up someone elses weapon.

Also, is it possible to specify attacks to different targets within one ATB bar?

e.g say I'm playing a healer and I want to use Cure on everyone on my team, do I have to break off each bar manually or is there a way to seperate the spells within one go?

You can't seperate spells to attack different targets in one go, no.

But you can do it quickly by pressing triangle when you have cure on say 2 bars (that'll heal one)....then by the time you choose 2 cures again you'll have 2 more bars ready for the next person.

But no you can't seperate spells in one go to affect different party members. 

I guess you don't have Cura yet.