So from my understanding, Marbury v Madison ruled that Marbury had a right to his commission, but that the Supreme Court could only decide the case as an appeal. So why didn't Marbury just take his case to a lower court that would have jurisdiction and then appeal to the Supreme Court if necessary? Did he somehow lose the right to the case after having "lost" it once, did he just not bother, or am I misunderstanding something here?
No, he and the other individuals in the same position still had options. In fact, Jefferson interpreted Marshall's opinion in Marbury as having, among other things, instructed any other court that heard the same type of dispute to rule against his administration.
I think the conventional answer is that the political situation had changed so much between Marbury's filing of the case in December 1801 and the announcement of the decision in March 1803 that there was no path for Marbury to take office. The elections of 1800 had been pretty close and 7th Congress' Senate (at that time elected by state legislatures) was about evenly split. The 8th Congress, which began in March 1803, had a huge majority of Democratic-Republicans in the Senate. This raised the possibility of impeachment and removal. This threat hung over any judge who might rule in Marbury's favor, any official who might comply with an order to deliver Marbury's commission, and of course Marbury himself if he ever took office. The failure of the Democratic-Republicans' effort to remove Justice Samuel Chase in 1804 might have altered that calculus, but Marbury had probably moved on.
Regarding official disobedience of a court order, avoiding this result is generally credited as a reason for Marshall's decision. He did not want to order delivery of Marbury's commission only to have the administration simply refuse and leave him with no way to enforce the order.
There is a very interesting article on the practicalities of Marbury's aftermath: Karen Orren & Christopher Walker, "Cold Case File: Indictable Acts and Officer Accountability in Marbury v. Madison," American Political Science Review (2013). The article explores the issues you raise.