Not allowing certain spells that the casters would always have up is putting a serious handicap on the casters that rely on basic precautions for their survivability. No wizard able to cast simulacrum and contingency would ever start a duel. Likewise, not allowing a familliar or a steed to a Paladin is strange. What about a beast master? The goal of such a competition is to see which class would be the best in a duel. Such a duel implies some rules, but should not lessen the power of a class.
Rules should be more about what would disqualify a contestant, such as leaving the arena, what is leaving the arena and if such spells such as etheralness, planeshift and even blink would be considered leaving the arena. The starting distance of duels should also be considered.
In brief, removing any capacity that would normally be made as a daily routine should not be removed. Otherwise you will not have a true picture of the power of a class.
I know that this vision is not popular as a lot of people will consider that this is favoring the wizards and sorcerers in a huge way, but this is a sad truth. Casters were and are still stronger at high level than a martial class. Especially if they win initiative and even more if they are out of range.
A cleric requesting a miracle would pretty much win immediately too as it would bring a solar to his help. Again, if said cleric wins the initiative.