I am a level 19 Subtlety Rogue on WoW, and I was wondering, what are the best base attributes for me to have, e.g. Strength, Agility, Stamina, and what are the best Melee attributes for me to have e.g. Damage, DPS, Haste. All answers are really helpful as I'm not that experienced at WoW, thanks!

start by pressing escape. Then go to start - shut down computer. Grab a friend and go outside. Thats easily the best thing to do in this situation.

For a rogue of all specs, Agility is your prime stat, As you advance in level you will notice haste and crit become more useful. at 19, having a decent amount of agi and stam will help you surrive mobs attacking you. When or if you plan on leveling to 85, Stats will change some
Being Hit capped at about 7-8%~ will insure all Special attacks land on boss level mobs(lv 88/??)
Agi will increase the amount your attacks hit for thus, increasing DPS. Rogues are a pure DPS class, your only role will be putting out alot of damage really fast.
Strength is not used for this class. Do not use Str gear it will not scale up your DPS.
Haste is good for some specs, and less for others. Mastery at level cap depends on the spec as well. these are all things you will learn leveling/reading up on the class. A good rogue guide is up on Elitist Jerks.com you can simply google "Rogue guide patch 4.1" or "rogue leveling guide" for leveling help and tactics.
to recap stats are Agility > Hit Cap = Expertise Cap > Haste > Mastery > Crit. this is at 85.
Note Hit cap is 7%~ Expertise cap is 26. these are stats used by raid level rogue players give or take, im not going to be any more technical. This should help you have an idea of what to look for on your gear. at your level it would mostly be Agi>Stam>Crit. seeing how the gear at low level does not have mastery/ or very much haste or exp.
Good luck i hope this wasn't to much :P
P.S. Never se gear with strength it wont work. I guarantee you that.

Agility is by far the most important as it increases your attack power, and crit rating.