100+ LEDs is more IO than any arduino can handle directly.
What might be more straight forward is to use an Uno and have it control two MAX7219 or MAX7221, www.maxim-ic.com
, matrix driver chips.
Each can handle 64 LEDs. Your control is to write data into registers. Each register represents 8 LEDs.
Otherwise, a string of shift registers that control 8 LEDs each (one LED per output) such as this, which controls 96 LEDs, could be another way to go.
Same idea - you write bytes of data to a shift register, with an LED per output pin. This board uses TPIC6B595, for high voltage/high current (>5V and 20mA) operation, intended for 12V LED strings. If you only need single LEDs from 5V, than 74HC595 will work just fine.
Other chips are also possible, such as TLC5940 from ti.com, 16 PWM'able outputs,
or WS2803, world semi, with 18 PWM'able outputs. Only source I've seen for wWS2803 is e-bay, guy in Niagara Falls selling them.