The thing about plotting for an RP as opposed to a self-contained novel or movie is that you've got to remember your players, and their interactions and motivations, will create and change the "original" plot. Unless you've talked to your players beforehand and planned out how things will go, in order to keep the plot on railroads, it's almost inevitable that what they do will change your setting, provoke your NPCs into different behaviors, or throw off your expectations and plans. And while you might need to reign in the chaos every so often, to me seeing those changes is part of the fun of being the GM the way interacting with the plot is part of the fun of being a Player.
The idea is that a group of people that had been under the wing at some point of a disgraced archaeologist who after dying, has given the group's control of what is left of his family's fortune and estate and have decided to carry on his mission and discover the lost history of the world. Starting with the finding of an artifact that the disgraced archaeologist was looking for. Anyone here willing to help me with this?
The essentials of any plot, imo, is that "A character Wants something really badly, but Can't Have It because X is in the way." So for an RP, you need to consider "Why do the Players want to carry on their mentor's lifelong goal" so badly? This means you'll need to put some sections in your Character Sheet for Backstory, and maybe Motivations or Personality, and try to work with what the Players give you. You can either leave "The Artifact" or "The Archaeologist's Mission" vague until you have a better idea of what kind of characters people are going to make, OR you could make it something that most people, in general, would want for some reason or another.
For instance, if the Artifact is worth millions of dollars, there are many many reasons Characters could want that money. "It belongs in a museum!" "I need to pay for my sick sister's extremely rare surgery!" "I want to clear my debt with the Yakuza before they take my kidneys!" And so on and so forth.
If the Artifact is said to have the power to grant wishes, or give a person control over others, or some other supernatural ability, that would likewise be a big motivator to a lot of people---BUT, it also opens the door for skepticism from Characters who wouldn't believe in its abilities, and thus they might not be as convinced to heed their deceased mentor's words. In other words, they might say "to heck with Dr. Indie's pipe dream, I'm taking my piece of his fortune and going home."
So, consider what it is you want the Players to do, and then consider how their relationships with each other, with their teacher, and with the Artifact could motivate them to do those things.
Next, the part where "They Can't Have It Because X is in the Way." Again, this one is much easier to do if you already have an idea of what kind of characters your players are making. If one player has in their Backstory, "parents were killed by a terrorist attack," then maybe you have a villain involved with that terrorist group who wants the Artifact because it's a "holy symbol" to their death cult or something. If all the Players thought of the Archaeologist as their father figure, then maybe the villain is a megalomaniacal female business tycoon who used to be romantically involved with the Archaeologist, but he left her for some reason and now she wants to "destroy his legacy."
Alternatively, if you don't have an Indiana Jones style race for the Artifact going on between Players and Villains, then you'll need to design whatever set pieces are in place to make the Artifact hard to reach. A deadly desert, an arctic wasteland, a temple full of traps and twisting mazes, etc. And to make these obstacles meaningful to your players it might be a good idea to include things that will force them to face their fears or question their own motivations--and, again, this will rely on your ability to connect their backstories and personalities into your original plot. For example, maybe one character is a brooding loner who hates relying on others for help...but then, how will they get past the puzzles in the ancient temple that requires them to have a team of people standing on different weighted pressure plates?
I hope this hasn't been too wordy, and that it helps you develop your idea! Good luck to you!
