I FIRST WANT TO SAY I DID NOT WRITE THIS STOLE FROM REDDIT, BUT ITS REALLY HELPFUL
Ok... starting as a member from ftp.
Buy a couple rings of dueling/games necklaces. P2P is huge, and walking everywhere sucks. In that vane, you are going to want to do the Lost City quest, Fairytale Part 1, and then start Fairytale Part 2, so you can access the Fairy Ring network, which really opens up where you can go throughout the game. Additionally, you're going to want to do the quest Plague City so you can teleport to Ardougne. Finally, you'll want to tackle the Gnome series of quests (starting with Gnome Village) so you can use the Spirit Tree Network.
Definitely try to start the Forgettable Tale of the Drunken Dwarf quest, so you can access the Blast Furnace. Smelting iron and mithril bars there is about 500k gp an hour, while adamantite bars are 750k and runite are about 1000k.
Other great skills to level up to make money are Hunter and Runecrafting. Runecrafting nature runes at the Abyss at level 44 is about 430k per hour, while at level 50 becomes 530k an hour. Sorry I don't have numbers for Hunter, but I can afk make about 400k an hour catching sabre tooth kebbits at level 51 Hunter. Red and black chinchompas are also really good money, both probably 500k+ per hour.
When you're watching tv or chillin or really want to "afk," start doing the Motherlode Mine. It's not the best mining xp per hour, nor the best money, but you're going to want the Full Prospector outfit eventually, and it's super easy to do. Make sure you unlock the upper level first, before getting the outfit.
The reason you want to do MLM is for the Falador Hard Diary, and the Coal Sack. Diaries are huge. After you secure some basic transportation stuff, definitely look at knocking out some diaries. The Varrock Diaries, for instance, give an armour piece that gives you a chance at mining double the ore, increasing profit/xp per hour. More importantly, every day it will allow you to purchase a private stash of Battlestaves for 7k gp each (they currently insta-sell on the GE for 8750 gp). Easy diary gives 15, medium 30, hard 60, and elite 120. That's that many * 1750gp profit every day you log in and buy/sell them (which literally takes 30 seconds). The Karamja easy diary is another great diary, as it gives an xp lamp that you can use for any skill, regardless of level (most diaries give lamps that require a minimum skill level). Also, the Varrock Medium diary lets you toggle your Varrock teleport directly to the Grand Exchange. The Lumbridge/Draynor diary is generally the easiest diary, and the Explorer's Ring can be helpful until you get your agility levels up. The Ardougne diary is also really great, giving a sweet cape that eventually becomes near best in slot for melee combat, and helps with training the Thieving skill.
And you should train agility. Learn to do it while you are doing other stuff, particularly high level alchemy, on items like air battlestaves or d'hide bodies. Do quests to get your agility up, but also train on rooftop courses, where you can collect Marks of Grace which can be used to buy the Graceful set, which reduces your carry weight and when fully complete recharges your run energy faster. Every 6 agility levels will increase the rate at which your run energy replenishes.
Another great transportation method is utilizing your house. It will take time and money, but a great goal is leveling up your Construction skill to 50, so you can hire a Demon Butler and build Portal Chambers. Portal Chambers hold 3 portals, and give you an infinite number of teleports to places you designate via 100x normal casting cost. Additionally having 50 construction with a Demon Butler opens up a great afk magic training/moneymaking method: making teleport tabs. You can currently get about 56k magic xp and 230k gp per hour making Falador teleport tablets. And you only have to click once every minute or so to do it!
As you go around the world, check out different minigames you come across. As you try them out, you'll often open up a free teleport to them once every 20 minutes, similar to the "home" lumbridge teleport. You can access this via the same tab as your quest log, by clicking the middle star.
Finally, after all of this, start doing Slayer. People here will tell you Slayer is the best money in the game (which it is not). However, it can be really profitable, and help you train your combat stats. The reason slayer is a good skill to train is because of the Black Mask/Slayer Helmet. When worn, it provides 16.67% increases to attack and strength, while you're on task, speeding up your training. Note that while your Slayer level is low, training this skill is going to be a real grind, and cost you money. At around level 70, you'll start to see your tasks making you noteworthy money. To get the benefit of a Black Mask for ranged and magic, you'll need to imbue it with Nightmare Zone points. You can get like 9 free Slayer levels (and Hunter levels) by completing the Varrock Museum quiz in the basement.
Set goals for yourself, and don't try to 'go infinte' off your first bond. It'll take a few before you really can, without grinding mindlessly for hours on end. But it's possible for sure to play this game for free, logging in for like 10 minutes a day. Have fun, and enjoy!