BY WAY OF WELCOMING Metro's excellent choice for the next general manager-the popular and highly qualified Richard S. Page-we think it's useful (though maybe just a bit depressing) to look at some of the tough issues that still-or, in time, will-confront the public system of the nation's capital. Most of them are quite familiar to Mr. Page, who comes to this job with an impressive record as chief of the federal Urban Mass Transportation Administration and, before that, executive director of Seattle's system. More important, he has been intimately involved in Metro's complex financial perils over the last two years; in fact, Mr. Page is given considerable credit for persuading the Carter administration to support the completion of Metro's planned 101-mile subway system.

The achievement, plus the first-class political/managerial job done by the outgoing general manager, Theodore C. Lutz, have kept this multi-billion-dollar public-works project alive if not always well. But Mr. Page will need all the political talent he can muster to keep the fragile coalition of federal, state and local governments financially together-not only to finish building the rail system, but also to pay for running the buses and trains.

As Mr. Lutz knows all too well, there's much more to the job than those endless calls on Congress and pleadings in Annapolis and Richmond. How do you get more people out of their autos and into buses and subways? It is financially unrealistic to think you can do this simply by drastically lowering or eliminating fares; the fares must bear some relationship to operating costs. Special subsides can be arranged for those riders who deserve a break: schoolchildren, the elderly and low-income residents.

There's something more fundamental involved here: the difficulty of using the system to get around town. Would-be riders-including many longtime area residents-are scared off because they can't even find out how to use Metro. Thanks to a talmudic fare schedule and a transfer scheme to match, the costs of riding a bus or subway are a total mystery to too many people.

Even when you do happen to have that unspecified exact change, how can you tell what route a bus takes when the only clue is "Trindad" (but not Tobago) or "Ga. & Alaska"? Anyone who's tried to find a decent map at a bus stop, or tried to telephone for some help, or didn't realize that the only hint of a subway station is an unassuming pylon with an M on it, knows how frustrating the Metro experience can be. Mr. Page and the Metro board also will have to keep a close watch on maintenance of the buses and subways, mechanical as well as custodial, the security of passengers and operations during heavy snow.

If all this strikes you as a tall order for the new general manager, it is. The job is considered among the toughest administrative challenges in town. Mr. Page says he's looking forward to the test-and it goes without saying that we hope he passes.