I won't go into rectifier designs (a bit dangerous to build from scratch for someone not familiar with them), but once you have rectified DC voltage, you really should consider using a current regulator (not a simple resistor) to output to the LEDs, you could easily run 10 strings of 30 LEDs from a 120VDC circuit, with a 1-ohm resistor in each string to help balance current sharing, off a 250mA output (slightly overdriven 25mA per 5mm LED typical, at a Vf of around 3.5 per LED) current regulator (a linear regulator capable of this would cost all of about $2 to build if mounted to the chassis as a pseudo-heatsink, a switching regulator would cost more obviously). Anyhow, you'd want to use a regulator because voltage sags and spikes on the line could cause havoc with a simple rectified/resistorized setup and result in blown LEDs, leading to blown strings and then a blown fixture (potentially in about 0.2 seconds total from start to end, more likely a slower but still eventual death one LED at a time at first.
In other words, for an extra $1.75 over basic resistors, you can run a much more reliable linear current regulator.
Still have to get the DC conversion done, best bet would be an off-the-shelf wall-wart or in-line converter of some sort.