This guide will be updated and adjusted accordingly as quests and achievements are added along the development path.
Magic: Training up magic may be challenging at the start before people start runecrafting and selling runes more or gaining chunks of money, but magic is one of the easiest ways to get to the center of main cities quickly.
Task System Rewards/Quest Rewards: Task rewards such as the Explorer's ring and the Ardougne cloak are excellent ways to quickly get to a few locations. To claim them, you must meet the minimum stat requirements to complete the diary you are claiming for and then speaking to the task master for the area.
Explorer's Ring (Speaking to Ned, Explorer Jack, or Bob in Lumbridge): Unlimited teleports to the cabbage patch south of Falador. Incredible for farm runs.
Ardougne Cloak (Speaking to the Town Crier, Doctor Orbon, or Aleck): Unlimited teleports to the monastery south of Ardougne and to the Ardougne farming patches. Another great farm runs item and a very quick prayer restore teleport.
Ectophial (Speaking to Velorina while meeting the requirements for Ghosts Ahoy): Unlimited teleports to the ectofuntus. Amazing item for farming runs and for training prayer before you have access to someone's gilded altar.
Drakan's medallion (South of Burgh De Rott bank underground inside the coffin after meeting requirements for Branches of Darkmeyer): Unlimited teleports to Barrows, Burgh de Rott, Meiyerditch, Darkmeyer, and the Meiyerditch Laboratories. Very quick way to get to Vyres (Darkmeyer), Mutated bloodvelds (Laboratories), and is a must have for the Barrows minigame.
Tokkul-Zo (Tzhaar plaza speaking to Tzhaar-Mej and meeting requirements for Elder Kiln): Unlimited teleports to Fight Caves, Fight Kiln, Fight Pits, and the central plaza in Tzhaar. This is the best item for utilizing fairy rings as it is the closest quick teleport to a fairy ring.
Enchanted Lyre (Crafting and enchanting it): Unlimited teleports to Rellekka, Waterbirth Island, Jatizso, and Neitiznot. Excellent item for getting to dagannoths and the dagannoth kings. If you have to gather snape grass for prayer potions, this is also great item to have.
Teleport crystal (Killing elves in Lletya and charging the crystals they can drop at Arianwynn): 4 teleports per crystal to Lletya. Pick up a bunch of these for quick access to the fruit tree or Elf slayer tasks.
Fairy Rings: Fairy rings are pretty immensely versatile and are a great way to get almost anywhere in the game very quickly. The dramen staff can be found near the shed in Lumbridge Swamp and must be worn when using fairy rings. There are too many locations to list here so here is a link to a list of the locations here.
Spirit Trees: Decent way of reaching a few unique locations such as the Poison Waste Slayer Dungeon, and the Grand Exchange. Quickest way to get to one is probably Mobilising Armies teleport and a close second is the Ardougne cloak teleport to the monastery.
Charter Ships: Charter ships are a fast way to get to each coastal port in the world. The only downside is that it can get a bit expensive to use them often as the price is a little costly early on when you don't have a whole lot of cash.
Making money is slightly difficult early on and is somewhat dependent on which XP mode you have chosen. This list will go from lowest requirements/effort to highest requirements/effort.
Thieving: Thieving is a pretty fast early way of making money. Silk stalls being the simplest option. Stealing silk and selling it back to the silk stall owner nearby in Ardougne is the primary early way of making money. Pickpocketing higher tier monsters or even a few of the chests is a great goal to have too if choosing this path. You can get rune battleaxes and hatchets from thieving the chests in the enchanted axe hut in 52 wilderness next to mage bank. Nature runes are pretty easy to thieve when opening the Ardougne chests as well.
Agility Pyramid: This method gains 10k gold per lap in the desert and is a decently quick early game way of making starter cash and training agility.
Making Battlestaves: You can buy soda ash and buckets of sand from the charter ship shops around the world and make them into molten glass. Blowing the glass into uncharge orbs, imbuing the orbs, then attaching them to battlestaves is a great way to train crafting and very profitable.
Woodcutting and Fletching: Fletching/stringing longbows and alching them or selling them to the general store is probably the least effort to reward ratio out of these starter options as it is quite afk and very rewarding at higher levels.
Slayer and Alching: Most slayer monsters will drop occasional rune armor/weapon drops that are alchable for some solid cash flow. Slayer is probably one of the best ways to make money in the long run as it has access to some of the best mid tier gear in the game such as whips, ganodermic, polypore staves, rune boots, dragon boots, etc. It also will help train combat stats efficiently if you are planning on bossing in the future.
Barrows: This minigame is fairly low requirements as all you need is some basic magic gear such as an Iban staff (purchased from the man at the entrance to the Underground Pass in West Ardougne) or a Slayer staff (Thievable from HAM members or buyable from a slayer master). If you get your reward potential to a decent rate with a couple killcounts each run, the number of runes you receive is pretty high. Selling blood/death runes to the general store is pretty rewarding.
Bosses: The bosses in the game are a bit more geared towards trading people in their profit as it relies mostly on selling rare drops for most of the profit, but they can drop a lot of alchables as well.
Pest Control: Gather a team of at least 5 players to defend the void knight. Earn enough void commendations and buy yourself a set of void or perhaps a bit of extra experience in your favored skill.
Castle Wars: Get together with a few people and enjoy a break from making gains. Strategize against friends in the ultimate game of capture the flag. Place barriers, blow up rocks, fire giant catapults... Do what you have to stop your foes from capturing that flag!
Fight Caves: Take on perhaps what could be considered one of the most difficult boss experiences in Darkan. Fight your way through 63 waves to obtain a fire cape.
Fight Kiln: Did I say Fight Caves was one of the most difficult boss encounters? Woops, Try taking on multiple TokHaar-Jads in this painstaking endurance test for the best in slot cape. Definitely a difficult achievement, but the rewards are well worth the challenge.
Sorceress' garden: Sneak past elementals and pick some Squ'irks from the forbidden trees. Crush them up into Squ'irk juice with a pestle and mortar, and a beer glass. Take them on over to Osman and get a tasty treat of some Thieving experience.
Stealing Creation: Another relaxing minigame that you and your friends can take a break from the gains with. Put together some teams and challenge each other. Who can collect the most resources? Or better yet, kill your enemies for their progress. Win enough, and buy yourself some rewarding gear that increases your experience gains.
PS: It is best to use OSRS quests guides, as RS3 has reworked some of their quests and the guides may be inaccurate.
Waterfall Quest: Quest Guide
Restless Ghost: Quest Guide
Cook's Assistant: Quest Guide
Gertrude's Cat: Quest Guide