Hello Allan, Beech and Oak are both fairly hard timbers. Having said that no timber can withstand a biro being pressed down hard on a single sheet of paper, that will always leave an indentation, so there's a responsibility on the user to show some common sense when using any wooden desk.
The photo you linked to is crying out for veneered MDF construction with only the actual legs and a few secondary components made from solid timber. Of course it's possible to make something similar entirely from solid wood, but that would be a big undertaking requiring fairly advanced machinery if it's to be completed efficiently.
You do need to be pretty sure of your abilities and commitment before tackling a piece like that if you're not to find yourself in over your head. Even in MDF, working in a typical home workshop, it's still a pretty big challenge. It might well take a beginning woodworker 150 + hours, require £200 plus in materials and fittings, and needs a method of cutting MDF to dead square, precisely sized components. If you're up for that then go for it, but if that reality sounds a bit daunting then maybe think about a simpler desk without the drawer cabinets?
I don't want to sound negative but I've seen plenty of newcomers embark on big woodworking projects only to end up abandoning them.
Good luck!