I've got the second limit break and it's quite great. It makes an instant kill in non bosses. Also, Aeris first limit break is a great tool cause it generates a lot of HP points for all my fighters.
I am not quite understanding how materia works and didn't know that it starts to level up. Currently I am using on Cloud, the lightning and cure materia, while in the others fire or ice. How can I get more spots to use materia with a single character (currently only Cloud can use 2 materia at the same time). Any hints and tips for materia, and which materia should I use would be appreciated cause it's my first FF game and I am not familiar with it. Also, can I equip multiple weapons in a single character, and does weapons level up or not. Also, a curios thing, does my companions that are not with me during the fighting level up or not? Hell, this game is a lot more complicated than I thought.
On another note, the story really looks great.
No problem.
Green materia give you spells. Fire, Ice, Lightning, Cure etc...
To that green materia, you can sometimes attach blue 'support' materia. For example, you can mix fire with 'all' (you need to have joined materia slots to do this as opposed to the individual slots you put them in), which means you can cast 'Fire all'. You can also get yourself Aeris' first limit break on any character in effect by attaching 'cure' and 'all' in the same slot. How many times you can use the effects of 'all' are limited to how many stars are lit up on 'all'. At this point, it's unlikely you will have any materia levelled up - it usually starts properly happening after Junon without any training. 'All' will not take long to level up for the first time though, and if you level it up fully you can sell it for 1.4m gil! This is the easiest way to make money on the whole game I'd say, although it will still take a fair bit of time even with the battles at the end to do it from scratch. You can eventually get hundreds of AP per battle though which will speed things up. When materia does level up, it will tell you after the battle.
Another thing, whether you put materia in the weapon slots or armour slot may effect the use of that materia. There is a materia for example called the 'elemental' materia (I think) which can be used to either add an element to your attack or defence. If you join lightning with elemental materia in an armour slot, depending on how levelled the materia is, you will either reduce or absorb lightning damage.
Pink materia usually has some sort of stat based benefit or combat based benefit. I'm guessing up to now the only one of these you'll have is the one in Aeris' garden (cover). You don't need to join these up with anything from memory. It doesn't matter where you equip these either.
Yellow materia will add a command to your list of stuff during battle, and you'll come across more of that sort of materia quite soon. There are a few of these that you can link up with other materia but these mostly work on their own in any slot. There are a few amazing pieces of yellow materia and one is to come up quite soon and should be equipped straight away. Would recommend asking on here about how to make it better unless you want to just go for it and strike lucky. It'll save going on the internet and trying to come across something without spoiling the storyline massively.
There is a really iconic moment in this game that is plastered absolutely everywhere on these sort of websites - it can even be found in this thread! 
There is another sort of materia you can equip too which I won't say anything about at this moment because you probably won't have it just yet. It won't require any explanation, though.
On whether you can equip more materia, with newer weapons and armour you will get more or less slots. These slots will have different growth rates as well, meaning that if you have a weapon with a 'double' growth rate, placing materia in that slot will give double AP to the materia equipped there per fight. Some weapons have no growth and should be avoided if you are trying to fit materia in to level up. Never put 'all' in a weapon or piece of amour with no growth. 'All' is your money maker later on in the game, but it needs to be able to level up. Weapons/Armour with no growth are quite rare though, to be fair.
Don't click it Revan, it's everywhere.