Level 1-8: train on rats and you will constantly kill them easily and you will gain xp (experience points) quickly.
Level 8-23:Train on goblins or cows and bring some food. For cows, kill in Lumbridge and bank their cowhide. Sell at the Grand Exchange and you will get a good sum of money. Buy some decent armor and weapons at you level.(Mithril).
Level 23-30: Bring 10 gp with you and half inventory of food. Trout recommended. Go to Al Kharid and train on the level 9 warriors in the main building.
Level 30-35: Train on the zombies in the draynor gutter, you will need a good amount of salmon.
Level 35-41:Go to Varrock and train on the guards. By now you should have at least 2 adamant armor pieces and a str. amulet. Or, If your attack is 40 invest in a rune scimitar. If not, stick to an adamant scimitar or battle ax.
Level 41-53: Train on hill giants.
Level 53: By now you should have completed dragon slayer and you have full rune and rune scimitar.
Level 53-65:Train on moss giants on Crandor. You can get there by entering the volcano in Karamja. Before you go to Crandor, go fishing, catch enough lobsters to fill your inventory, and cook them. Then begin your training.
Level 65-75: You should be a member now. Train on the spiders in the Stronghold of Security.
Level 75: By now you should have decent armor, at least some pieces of dragon, or if you can afford it - barrows / 3rd age. A weapon such as a whip / Godsword is also recommended.[you can use a whip to train strength but is extremely slow & trains attack, strength, and defence all at once and a Godsword is too slow, a dragon scimitar is the best option]
Level 75-85:If you have done monkey madness, go train on the monkey guards, you should pray fighting them.
Level 85-99: Armored zombies are the best here, for power leveling, otherwise slayer is a good alternative.