n.B: I'm using SFoS fleet build rules --- because I don't have Armageddon with me and I really don't like the new fleet build system. Natch.
Centauri is an excellent beginner fleet. The tactics are direct and uncomplicated. You can even avoid a cheese build with a little simple work, and try to keep the cost down.
As to the Centauri fleet box -- for a balanced fleet, don't. You'll get a lot of Vorchans you don't want, or need. But, just next door is the first good ticket, the reinforcement fleet box. Dargan, two Maximus, 2 Darkeners and a boatload of fighters for $50/£30. Ching! You won't use the Kutai, but the Raziks will be your fighter cover when you don't take a carrier. The Rutarians can be a later upgrade if you want 'em .... I'm not totally sold on them.
That's 3 raid already. (Dargan, Darkeners, Maximii). You need two more. Cheapest way to get there? Primus. You'll also use it religiously for War-level fights anyways, so, why not. And, if you get bored with it, you can call it a Secundus, which flies very differently. If you're getting whupped all the time, you can call the cheese out and call it a Tertius (if you can stand the accusations).
If you're out to build 5 War as well, it'll cost you more cash. At this point, you have to start to seriously think about the Centauri base fleet box. Yeah, it's $100/£55, but you'll want the 2 Primus and 2 Centurion. The Vorchar makes a nice scout, but you don't need 6 of 'em? The other options are poor (the Vorchat) or downright stupid (the Demos). The box's value really depends on the fighter contingent. If you're OK with fighters as counters, buy the capital ships individually (total $60/£34).
The Darkeners and Maximii make 1 War. A couple of Primus make two. The cheapest way to field War is to get an Octurion, and at $20/£12, it's dollar-effective nasty fleet unit usually worth buying. That's your third war.
Two Raid and two Patrol is another War point .... and if you have the Fleet box, you have 2 Centurions already. You just need two Patrol. Enter the Corvan, the fleet scout you desparately need. $9/£5 for a patrol point sounds expensive as all get-out, but this thing is worth it. That's your fourth War.
If you didn't get the fleet box, you'll want those Centurions anyways. Pricey, but nice figures. Resist the cheese temptation to make these Prefects, unless you face equal and opposite cheese.
You have one Dargan, so another 2 Raid makes sense. While some folks think its cheese, you're just starting, and few people will begrudge you a couple of Sulust. At $9/£5 each, they're pretty cost-efficient.
5 War on a total budget of $166/£96. ($206/£117 if you want fighter minis and bought the Centauri fleet box together with some Vorchan figs -- they are useful in Skirmish-level fights, don't get me wrong -- you just almost never need 6!)
5 Raid on a total budget of $65/£38.50.
Eh. No one said getting into minis was cheap, but this is a very very flyable, and learnable fleet, for a (what I consider) reasonable price that'll fly reasonably against most everything. The Raid stack is very front-towards enemy, and an ISA player will give you nightmares. Against Minbari, the lack of a scout at Raid will hurt like the dickens. Against everything else you should be OK. And, if you use Armageddon, you have sitting aside the Balavarin/Balavarix from the Reinforcements box as fighter cover, just waiting for the "go" signal.
Of course, if you're really saving money, just use the counters, and build away. You can easily experiment with the Altaran/Elutarian/Magnus, which are all very buyable Raid ships.