Build one of the rockets from the Proton family, build a fully recoverable Starship that can land on Mars and return to Earth and build a cool looking rover that has multiple functions, all up to you.
I have a mission suggestion as well: Build a space station around Mars.
Rules:
No...
Kim Stanley Robinson's Mars Trilogy are my favorite sci-fi books. I enjoyed reading them, and their quite long books with each page being a literal wall of text. I would recommend taking a look at them.
The biggest design problems are protecting the engines and mounting a shield that both covers the belly of the shuttle and allows the retractable (not sure if it even can) landing gear.