You DEFENITELY do not want to buy the starter pack. 
for a CV Crew you should have
:
6-8 Fighters (Mininum 12+ Base)
1 Seaman with Good all around Potential base and Fighter base
1 Engine Because you need that speed to get out of certain situations
2 Bombers ( If you're going to play in CV select rooms)
Optional
1 Rep
1 restore for 900SD
A pair of gunners to fend of dem subs 

Well, first you need to choose your nation. What nation you choose and for whatever reasons are totally up to you. For example, I have 2 CV crews, KM cos I think the CV6 is boss, and UK because I also wanted a TB orientated crew.

Since you mentioned fighters, USN has the best fighter aircraft and pilots. After them, France, Germany and Italy also have quite strong fighters. All nations fighters are useable if made properly however.

After that, you need to establish your crew setup, like deathaddict mentioned.

If you want fighters only then you'll want 8 fighters, but a fighter focused crew with 6 fighters and 2 bombers is my own preference, and like death mentioned youll need bombers to play in CV select rooms if you so choose. As mentioned, +12 fighter atleast.

KM and SN make better use of dive bombers, RN and RM should use torp bombers. IJN amd MN can make good use of either though the preference remains DB, and USN starts with only TBs but can then change those TBs to DBs which are better for USN. The higher the bomber stat the better, aiming for +12 again is good.

You'll also want a seaman for a fighter orientated crew, general consesus is that a seaman with good fighter will have more impact.

If you elect to level AA gunners, which can all also use HH, then you'll want to read how to level them effectively for US, RN, IJN and KM. Other nations have straightforward gunner classes that can use everything without the need for complex classing.

KM, MN and IJN have particularly strong AA. Though most CVs use their gunners for hedgehogs.

To level your crew properly, rotate the highest level sailors with your lowest level ones, so your lowest level crewmen are onboard at all times. This allows you to level the majority of your crew evenly (expect maybe your BO). Consider the level of your lowest level crewmen when choosing wether to move onto the next ship, get too far ahead and your lowest sailor will start to gain less exp for being too low.

A seaman for a Fighter Cv should have 12+ as a fighter stat and be boosted ( a nation +2 Fighter bonus also helps).
Any other stat that might be high is nice, but it will not help your fighters perform any better.
I'm sure I posted a link to the evidence somewhere on these boards, but I cba to find it atm.

Dont buy the starter pack.

Money making CVs only go for fighters.

To start from 0... Roll 5 to 7 Fighter Pilots based 11 and/or 12 in Fighter base. If you can boost them will help you more.

A Seaman, with high base in Potential and Fighter stats. (I dont use one).

And a Medic to reduce crew deaths, since CVs are the most vulnerable ships to lose rookies and experts, i lost a few vets sometimes. I use a Medic based 14 Potential + Boost, works wonders, rarely i lose sailors since i started using it.

Unless your a rushing CV, Engineers, Repairers, Restorers, SD is not important, once you get in BBs range its game over and even more over if your team is losing

My USN CV setup is 3 FPs 3 DBs and a Medic, im missing 1 sailor for my CV tho, i make 50 to 100k credits each battle. If you want more just go for a fighterwhore CV and spam them all over the game.

All above is asuming you dont want to use a credit card. In case you want to use it just buy 9 Elite Fighter sailors, 1 of those goes for seaman, and 1 Elite potentail for medic. Add a few boosts to the count, then roll out a base 13 or 14 potential for the BO and a couple based 11/11 or 12/11 gunners and you hae your CV crew ready. 

Lots of good advice here. I will only add/stress that you will want to take the time to roll +12s. +11 bombers later on will be ok, but if you roll and level +11fighters you will wish later on you had invested the time in making them 12s.

BVE is a must to be competative with your fighters. Also read the CV guides and properly micro-manage your planes. You wont be able to go head to head with fighters 20+ levels higher than your own, but you can micro yours and still provide vision for your team against higher levels.

A good restorer will allow you to take some extra damage before you die.

A high level +12fighter stat Seaman can and will provide a 5% boost to your fighters at end game levels.

Mentally prepare to get owned alot by CV6, PCV, CV5 while you level from 55-85.

Regards,

Nik

Not sure how far you want to go, but if you plan on a CV6 eventually, you need:

Level 120 BO
Level 120 Gunners (2)
L110 supports (8 pilots, 1 Seaman)

As you progress, the guns on all CVs are lousy. HH, and especially PHH provide significantly more devastating firepower across the board.  Range and destruction, plus anti-sub too. 

You'll need gunners, fighters, bombers and supports to some degree and getting all of them upleveled at the same rate is really tough.   I like the idea of going with AA gunners as most good AA guns are dual purpose anyway. 

Chief Seaman makes the most sense.  Engineer also, but running is usually the end of the game anyway. Repair, Restore?  I just add as much armor as possible.

But the PCV is the best CV available for most players. Almost CV6 capable (11 vs 12 lifts), and enough planes to ride out a Great Battle. Doesn't have the same restrictions.

All of this has been good advice.

As you get to higher CVs with higher lvl pilots, you might go something like 4 bombers and 3 Fighters.    You can then "railroad train" flights of bombers with fighter escorts.   As soon as a bomber plus  fighter flight leaves, refuel another flight.   By the time the first flight gets to the target the second flight will be ready to lauch.   Hit your target, launch the next flight, and fuel the third.  

By this time the first flight should be back and you start the cycle again.  You have continous flights in the air.   You can have 16 to 18 planes in the air easily.

If you micromange, your escort fighters will intercept the enemy interceptors and your bombers will get thru.     This is the way to sink high lvl BBs and CVs and gain super experience points and credits.

Doing this will keep you extremely busy and you have to hope your team mates are covering you with AA and ASW.

Just another method of playing CV.