Spell Speeds? Well, there pretty much covered in the basic rule book which you can download at
www.yugioh-card.com as a PDF file. But basically, they determin what can and can't be chained to each other. Spell Speed 1 cannot be chained to each other unless the activate at the same time. Spell Speed 2 can only be chained to another Spell Speed 2 or lower. Spell Speed 3 can only be chained to another Spell Speed 3 or lower.
Normal, Continuous, Field and Equip Spell Card are all Spell Speed 1 for example and can only be activated during your Main Phase. Traps are all Spell Speed 2 and can only be activated on your opponent's turn. Counter Traps which are Spell Speed 3 are the only 3s in the game. Monster effects can only be 1 or 2.
Priority on the other hand is a different can of worms altogether. There are countless threads here in the rules sections discussing that subject. Priority is, very basically, something players have. Not monsters. When it's your turn, you have priority to activate effects or take actions first during a given phase before your opponent can respond. Only when you do something or pass can your opponent do something on your turn. For example, when you summon a monster, once the summon has successfully completed, you retain priority to activate Spell Speed 2 effects, the effects of the Monster you just summoned, or the effects of a monster you already control. You either do one of these or pass. Only then can your opponent respond to the summon. Some effects trigger as soon as a summon completes, like Breaker receiving his Spell Counter. In those instances, your priority effectively gets used up by forced effect and your opponent gets to respond to the summon and in chain to the effect.
Priority and Spell Speeds are simply two different operations that determine who gets to go first and with what effects they can respond. They are very important mechanics of the game that I would encourage you to research if play the game often. Yu-Gi-Oh! is not a game of who gets to flip his cards faster then the other. Priority determines who gets to activate certain effects first. And Spell Speeds determine what can be chained to those effects or activated in response to those events.