Here is one of the quickest and cheapest ways to get alchemy to 300: 
Skill Required: 0 
Skill Acquired: Apprentice 
Training Locations: 
Iron Forge, Stormwind, Darnassus, Loch Modan, Teldrassil, Elwynn Forest, Undercity, Thundering Bluff, Durotar, Orgrimmar, Trisfal Glades 

Skill Required: Alchemy Skill 1 
Max Alchemy Skill To (with the learned recipe): Alchemy Skill 65 
Recipe (Ingredients): Minor Healing Potion (1xPeacebloom, 1xSilverleaf) 
Approximate Cost: 65xPeacebloom (1.5g), 65xSilverleaf (3g), 65xEmpty Vial (11s) = 4.61g 

Skill Required: 50 
Skill Acquired: Journeyman 
Training Locations: Iron Forge, Darnassus, Ashenvale, Duskwallow Marsh, STV, Undercity, Tarren Mills, Orgrimmar 
Cost: 40s 

Skill Required: Alchemy Skill 65 
Max Alchemy Skill To (with the learned recipe): Level to 90 
Recipe (Ingredients): Lesser Healing Potion (1xMinor Healing Potion, 1xBriarthorn) 
Approximate Cost: 25xMinor Healing Potions (0g), 25xBriarthorn (1.75g), 25xEmpty Vial (4.5s) = 1.80g 

Skill Required: Alchemy Skill 90 
Max Alchemy Skill To (with the learned recipe): Level to 115 
Recipe (Ingredients): Elixir of Wisdom (1xMageroyal, 2xBriarthorn) 
Approximate Cost: 25xMageroyal (1.25g), 50xBriarthorn (3.5g), 25xEmpty Vial (4.5s) = 4.80g 

Skill Required: Alchemy Skill 115 
Max Alchemy Skill To (with the learned recipe): Level to 130 
Recipe (Ingredients): Healing Potion (1xBruiseweed, 1xBriarthorn) 
Approximate Cost: 15xBruiseweed (1g), 15xBriarthorn (1.5g), 15xLeaded Vial (6s) = 2.56g 

Skill Required: 125 
Skill Acquired: Expert 
Training Locations: Darnassus, Undercity 

Skill Required: Alchemy Skill 130 
Max Alchemy Skill To (with the learned recipe): Level to 155 
Recipe (Ingredients): Elixir of Defense (1xWild Steelbloom, 1xStranglekelp) 
Approximate Cost: 25xWild Steelbloom (3.5g-5g), 25xStranglekelp (2.5-4.5g), 25xLeaded Vial (10s) = 6.10g 9.60g 

Skill Required: Alchemy Skill 155 
Max Alchemy Skill To (with the learned recipe): Alchemy Skill 195 
Recipe (Ingredients): Greater Healing Potion (1xLiferoot, 1xKingsblood) 
Approximate Cost: 40xLiferoot (5g), 40xKingsblood (8g), 40xLeaded Vial (16s) = 13.16g 

Skill Required: Alchemy Skill 195 
Max Alchemy Skill To (with the learned recipe): Alchemy Skill 215 
Recipe (Ingredients): Elixir of Agility (1xStranglekelp, 1xGoldthorn) 
Approximate Cost: 20xStranglekelp (4.0g), 20xGoldthorn (9.0g), 20xLeaded Vial (8s) = 13.08g 

Skill Required: Alchemy Skill 215 
Max Alchemy Skill To (with the learned recipe): Alchemy Skill 235 
Recipe (Ingredients): Superior Healing Potion (1xSungrass, 1xKhadgars Whisker) 
Approximate Cost: 20xSungrass (8g), 20xKhadgars Whisker (3g), 20xCrystal Vial (1.0g) = 12g 

Skill Required: 225 
Skill Acquired: Artisan 
Training Locations: Feralas (Feathermoon Stronghold), Swamp of Sorrows (Stonard) 
Cost: 4g 

Skill Required: Alchemy Skill 225 
Max Alchemy Skill To (with the learned recipe): Alchemy Skill 226 
Recipe (Ingredients): Philosophers Stone (4xIron Bar, 1xBlack Vitriol, 4xPurple Lotus, 4xFirebloom) 
Approximate Cost: 4xIron Bar (1g), 1xBlack Vitriol (50s), 4xPurple Lotus (30s), 4xFirebloom (50s) = 2.30g 

Skill Required: Alchemy Skill 235 
Max Alchemy Skill To (with the learned recipe): Alchemy Skill 265 
Recipe (Ingredients): Elixir of Greater Intellect (1xBlindweed, 1xKhadgars Whisker) 
Approximate Cost: 30xBlindweed (10g), 30xKhadgars Whisker (5g), 30xCrystal Vial (1.5g) = 16.5g 

Skill Required: Alchemy Skill 265 
Max Alchemy Skill To (with the learned recipe): Alchemy Skill 280 
Recipe (Ingredients): Elixir of Greater Agility (1xSungrass, 1xGoldthorn) 
Approximate Cost: 15xSungrass (6g), 15xGoldthorn (3.0g-4.0g), 15xCrystal Vial (75s) = 9.75g 10.75g 

Skill Required: Alchemy Skill 275 
Max Alchemy Skill To (with the learned recipe): Alchemy Skill 275 
Recipe (Ingredients): Transmute: Arcanite (1xThorium Bar, 1xArcane Crystal) 
Approximate Cost: 1xThorium Bar (30s), Arcane Crystal (17g), Recipe (1.5g) = 18.80g 

Skill Required: Alchemy Skill 280 
Max Alchemy Skill To (with the learned recipe): Alchemy Skill 300 
Recipe (Ingredients): Major Healing Potion (2xGolden Sansam, 1xMountain Silversage) 
Approximate Cost: 40xGolden Sansam (16g), 20 Mountain Silversage (12g), 20xCrystal Vial (1.0g), Recipe (1.5g) = 30.5g 
Location: Winterspring Vendor: Evie Whirlbrew Timer: 3 hours Limit: 1 

Total Approximate Cost (minus the training costs) = 140.36g 144.86g 
Cost Differential (for servers): 15g - 25g 
Total Approximate Cost with training costs and server pricing adjustment = 155.36g 169.86g 

Dont buy anything else unless you want the recipes. The low end recipes are completely useless for power-leveling purposes so skip as many recipes as you can. Agility, healing, and mana potions tend to sell pretty decently and since you arent out to make a profit while leveling, these potions will actually help you recoup some of the money you spend.