Hi Dorantana, and welcome to the fold, I hope you will be glad you chose the red pill
I'm a relative newcomer myself, but I've spent quite a lot of time on the Infinity forums and researching things to buy (eventually settling with Haqqislam. .... and Nomads.. and Combined Army

)
so hope I can offer some good advice.
Is this faction fun to play? Competitive? Give me the low down.
With the factions of Infinity, there is less of an obvious difference than there might be say between orcs and space marines. Most armies have a light infantry, medium and heavy, as well as
TAG which are roughly analogous. So, a Nomad Heavy Infantry will be roughly equivalent in effectiveness to a Yu-Jing of the same class. That being said, some factions have a focus towards certain areas; Nomads have some good hackers for instance, and other 'pixie tricks', PanOceania have got a slightly better shooting, while Haqqislam have got very good healers (thanks to high willpower) and a predisposition towards many light but quite durable infantry.
As for 'fun' stuff, I guess that's a bit more subjective, but in terms of some of the more interesting Haqqislam stuff, you have:
Hassassin: Disguise yourself as enemy trooper, walk up to enemy soldier, kill them and then use their gun to shoot their friends
Ghazi Muttawi: Not very
PC, but having impetuous troops running towards the enemy and then 'self destruct' with
EM pulse is always entertaining.
Lasiq: I guess not really 'fun', but there is nothing cooler than someone running a distance away and then being taken down with a single shot from her viral sniper rifle.
This is 300 pts and is what is recomended on the site.
Definitely for normal games, but to begin with it is generally recommended that you start with a lower amount. The rules are fairly intuitive, but can get difficult with all of the special rules until you get used to it, so it might be an idea to start with just some basic light infantry and perhaps a special weapon of some sort. Then, later on start including the more 'special' options (thermoptic camouflage, guided weapons that kind of thing). But, as you say you are starting out with one of the starter packs you should be OK in that regard.
If you don't have it already, I would also recommend the online army builder (also downloadable) which is very handy, if you click on an ability it links directly to the Infinity-wiki which will give you the special rules:
http://infinitythegame.com/dt_army/
http://infinitythegame.wikispot.org/Home
As for something being 'competitive', again I wouldn't worry about it too much if you just get an initial purchase. The game is far less list-driven than the
GW core games - generally, unless you go stupid and make up an army of all one type, and you have some options, then there won't be any games decided before you roll a dice. I will say that the Maghariba, being a
TAG, is a case of putting quite a few eggs in one basket. It's not what you might call a high-end
TAG, it is cheap compared to others, but 300pt games might be won or lost depending on how well it performs. Correspondingly, it might limit your tactical options a bit. That being said, I have heard they are great fun to use, and of course for any fans of Ghost in the Shell they are a necessary purchase.
Hope that helps, like I say I am still a bit of a beginner myself, so I'm sure someone else can offer you some further advice.