I wouldn't even try to build a speed team for the arena if I were you, especially since you're having trouble gearing your champs and selecting the ones you want to use in the first place. There's always going to be someone faster than you, and since you dont have the speed stats to make yourself faster, than just build your team to survive the nuke.. HP and DEF gear is already available to you, and most teams dont have enough ATK and Crit damage to wipe an entire go second team that is competently built.. use champions that have ally protect, increase def, DEF based damage, and use a Void as your nuker if you have one..
Shield sets are amazing if you're having trouble getting enough HP on your champs... build speed into your champs by all means, just dont expect to go first then you will never be dissapointed with your team..