Ryu has entered the third World Warrior tournament in order to fight people! What a surprise! He fights Alex and defeats him, which causes Alex to be obsessed with becoming stronger. He does other things in the Street Fighter 3 series but that's about it in 3rd strike.
If you like playing generic characters with no personality and a totally bland (but solid) fighting style, you might be a terribly boring person. You are also probably going to love Ryu.
Super Art Selection - If you're a defensive player, you probably will prefer the meter that SA1 offers. If you prefer a riskier offensive playstyle, SA3 is the choice for you. SA2 has setups and does a buttload of damage, but is generally considered his worst super since it doesn't offer anything new to Ryu's arsenal (like Denjin) nor does it give enough meter to abuse EX moves (like SA1). All of Ryu's supers are usable with practice.
Normals - All of Ryu's normals are great. Notable normals include c.MK, which can combo into Hadouken or SA1. f.MP hits overhead. f.HP can combo into basically everything Ryu has. s.LP is Ryu's optimal anti-air, but doesn't always have the hitbox you'd like. s.HK and c.HP are other good normal anti-airs. j.MK crosses up. j.HP is your most damaging jump-in, but j.HK has the most range. j.MP is Ryu's best air-to-air since it hits twice and knocks opponents away.
Game Plan - Ryu's playstyle changes drastically depending on the Super Art selected. SA1 is typically a defensive or balanced style that allows the use of many EX moves. SA2 is a slightly more offensive style that relies on hitting SA2 to get the big damage in. SA3 is the most offensive style, which revolves around setting up SA3 and stunning the opponent.