I have to admit, a bike computer keeps me from getting a bit bored. Seeing how many miles you have ridden, tracking average speed, how fast am I going on this down hill, how long is that doggone long grade, etc.

What is a must? Safety items:
Helmet
Gloves; if you fall you don't want to scrape your hands
Eye protection? I wear glasses and I see plenty of people biking without any glasses, so I don't know if these are mandatory
Water bottle and cage, or camelbak because you need water
Bright lime green safety vest, which is also optional, but will help you be seen better

Not getting stuck in the middle of nowhere with a flat tire:
Frame pump
Spare tube
Patch kit, in case you get multiple flats)
Tire levers
Pair of latex/nitrile gloves to keep from getting dirty, greasy hands when repairing flat
Seat pack to hold all this junk

Everything else is as you see fit depending on how you ride. If you start taking long rides (15-20 miles), you will want moisture wicking clothing. Bike jerseys can be bought fairly cheap. Padded cycling shorts to prevent chafing and add comfort. You stock up on these on sale AFTER the summer season. As winter is mostly behind us, you don't need winter clothing. But it's all on sale now :-) If you are going to ride in the rain, you would probably want full fenders to keep dry. I have a multitool but I've never used it on the road. At home, I have real tools.

Most of these items will be a one time investment. Well, five thousand miles minimum :-)