You will have sufficient fire power with you primary and secondary schools. But you might want to purchase a larger deck with 25 to 30 cards capacity.
I like Balance with Death with balance having all the shields and death with its vampire to damage and heal at the same time. I only loose to a better armored opponents, or those of higher levels. But I got up to captain on level 16
Next is Myth with Ice, with all of Myth's minions and free minion shield from secret shop in krotopia, and ice's shields these combination is a winner! Again, at level 16
this is a school question, by that I mean certain schools can jump in earlier then other schools. for example myth can start as low as level 10, i know because i have done it several times, with a pip free minion myth characters will find themselves captians and commanders before they start facing other players who are 10 level or more higher when this happens step out, go get some more levels, then check back an see how you do. if you continue to be get beat then step out again do not lose your title trying to win. another example is balance while balance can step in early they really come into their own with judgement there is no denying that facing a balance player wielding judgement puts the pressure on to win and win quick. A lifer with shields is truly annoying they draw the game out and force you to either kill them in one shot or run out of cards and forfit
the reason so many high ranked players are storm, ice, balance, and myth is that these classes can either take a hit, dish it out, or in myth`s case strip you of your defences and then follow through with his doggy.
the other thing to concider is being part of a team, most teams do not work well together because they are not friends they do not feed each other bonuses of set the bad guys up for multipule attacks at once stripping their oppenents shields for their teammates. but teams that do these things are pretty unstoppable. three storm temptest in a row can be pretty destructive, a life player who heals and shields (instead of trying to cast a secondary school spell) can save a team from destruction.
everyone should step into the areana early and see how they do, at the very least they will learn to kill monsters quicker and get ideas for what spells they want to aquire for their deck before they step into the areana again GOOD LUCK