Dice

I love dice. They are simple herald's of fate, life, death and the physical embodiment of random herself. They've gotten me through critical strikes, plagues, and even a math test (don't ask). Realistically you'll need a full set for every player. I've played with one set shared among all players and so long as the group is small you might get a full set of the seven to work. Well technically if you use some basic division and ignoring the d"100" you only really only need a d12, d8, and a d20, and I guess if you worked with some probabilities you could play with only a d20. And technically with a computer you can find dice rolling programs so you really don't need any dice at all... Sorry, I got off track there for a minute.
Now realistically each player needs at least a full set. Rogues will need a pile of d6's and depending on what kind of character you're playing you might want more. Rolling and interpreting dice takes time so it's your job to maximize money spent on dice/ time spent rolling them. It might not take long to roll 2d6 with only one d6 but once you need to start rolling 5d4 for magic missiles you're gonna want to pick up some more dice. If its a one time influx of dice needed you can usually just nab an extra from a fellow player for a second without them noticing.
DMing's another story entirely. Since you're going to be rolling more dice in weirder combinations a starting DM's going to need at least two full sets of dice. That will deal with a lot of monsters quickly but just in case I usually have three to four sets behind my screen, or at least two and several extra d20s. Depending on what you're running your needs might change. Percentages are fine using two d10's but if you're running a plague campaign or a random romp through the wilderness invest in a zocchihedron (go look it up, its not perfect but its still darn cool) or learn how to get a random percent on your calculator/ computer. Also pack a big fat coin in your dice bag, it'll speed up 50/50 chances. I know these sound like pretty minor minimalistic time savers but after 6 hours of the same drawn out encounter you'll want to get quickly to the players' turns so they don't lose interest. Trust me I'm a self-proclaimed doctor.