Consider doing slayer. If you plan on maxing out your account, doing slayer alongside your melee stats may be worth it, as it will level up both skills at once. This will also give you access to some of the better monsters in later game that require high stats, such as abyssal demons.
Levels 1-10. Your methods here are similar to that of free to play. Kill goblins, mountain trolls, or even consider cockroach drones for their common gem drops.
Levels 20-30. Kill cockroach workers. They give decent exp per kill, and have noted ore drops, as well as very rarely dropping the coveted rune scimitar. These are found in the Stronghold of Player Security, accessed by a crevice in the ground south of Edgeville next to the Soul Wars portal.
Levels 30-40. Kill Cockroach Soldiers. These are located in the same area as workers, they drop rune items very commonly, and even have a chance of dropping medium clue scrolls. They give surprisingly good exp for how low of level they are, and good drops as previously mentioned.
Levels 40-60. Teleport to Caste Wars via a dueling ring and head East. Here you will find a lot of ogres. They drop seeds often, as well as a high rate of gold charms, higher than rock crabs. They don't really drop much else, but their exp is great. Alternatively you could kill moss giants west of Ardougne.
Levels 60-70. Kill Hellhounds in the Taverly Dungeon. You will require a dusty key in order to access the area, or you could have 70 agility to use the shortcut to go to blue dragons, or 80 agility to use a shortcut directly to the hellhounds themselves. Using a Guthan's set or Vampirism aura negates the need for food, as well as soul split, but it is unlikely to have that. A charming imp may help, as they have one of the highest gold charm rates in the game.
Levels 70-80. Consider getting 85 dungeoneering to access frost dragons. Not only would this give you chaotic weapons for later on, but they would give you access to this amazing money making and exp rate in the game. If you would not like to do this, travel south of the Bandit Camp to the Exiled Kalphite Hive and kill Exiled Kalphite Guardians. They drop blue charms and herbs frequently, as well as hard and elite clues.
Levels 80-90. It is highly recommended to have a high slayer at this point, as almost all high exp giving monsters require 80+ slayer. If you have this, kill abyssal demons or Spiritual rangers in the slayer tower and GWD respectively. If you do not, kill waterfiends by teleporting to Barbarian Assault and then running south and jumping into the whirlpool after completing barbarian training.
Levels 90-99. Again, a high slayer level is almost necessary. If you can, kill Airut for some of the best prayer and combat experience in the game, as well as dropping razorback gauntlets, bring in a hefty few million per drop. Automan tracers after completing The World Wakes is also very good with 95 slayer, as they drop noted high priced items like magic logs and sharks. If you cannot kill these, kill General Graardor in the God Wars Dungeon with his minions, or continue on waterfiends.