I would like to wire 7 banks of 15 LED's with each bank lighting up sequentially (one at a time, like KITT in Knight Rider).
Assuming it's one bank at a time, a standard Arduino (using ATMega328) would be fine. But let's say you want to be able to control the 105 LEDs individually, than you'd need a 128 bit decoder (a single 7 to 128 bit decoder is quite rare, but you can chain up multiple smaller decoders, for example 4 32bit 5 to 32 decoders) in order to be able to utilize the limited number of pins ATMega328 has.
That said, you can relax the requirement for the number of decoders required and go for a higher pin count chip (i.e. Arduino Mega), but even with Mega, you will still need to multiplex some pins since it only has 70 usable pins.
You'll also need to use some kind of LED driving circuitry since 100 plus LEDs can easily consume 1A or more current and the on-board power supply will not be able to handle that load.
I'd suggest you search this forum for Knight Rider and see what approaches other people had tried.