The least expensive LEDs that already come soldered to cable assemblies with JST plugs are the ones from YeahRacing (series LK-0008 for 3mm LEDs, LK-0009 for 5mm LEDs - RCMart usually has a full selection). Even better, the YeahRacing LEDs come with current-limiting resistors already installed in the cable so you don't need to include them on the board (in which case you can just jumper across the resistor position on the board with a small piece of wire). Other brands that work are 3Racing and Tamiya but these do not come with current limiting resistors (so install them on the board). All three of these brands use the same plugs and the same polarity.
However you can use whatever LED you like. The Bill of Materials lists the part numbers for the JST plugs if you wish to make your own cables (or you can solder the wires directly to the OSL board and skip the connectors). You can also buy pre-made JST cables on eBay for very little money, do a search for something like “PH Female Connector Leads.”
Tests were done with the OSL through-hole board (v1.7) using the transistors specified in the schematic (BC337) and it was found each output could source approximately 500 mA of current. Most LEDs draw far less than this, usually in the range of 20-50 mA.
LED Current Limiting Resistors
Most LEDs run at low voltages and require a current limiting resistor. The value of the resistor depends on the LEDs you are using and the amount of current you want to allow.
Typically the LEDs available in the RC Car market today come in a string of two LEDs per cable, wired in parallel. Unfortunately specs are rarely listed for any of these products. The YeahRacing LEDs are unique in that they already come with a current-limiting resistor installed inline so these don't need an extra resistor on the board, and if you don't know what you're doing it is recommended to use them.
Otherwise if you are unsure what resistor to use, testing has found that most pre-assembled RC LED cables will work with a series resistor of 100 ohms even if operating at 6 volts. If you wish to maximize the light output you may go to a lower resistor, say 75 or even 50 ohms. However be sure to measure current draw with a meter - you shouldn't usually exceed 20mAh per LED, which would be 40mAh total for a string of two LEDs in parallel. If you want to be safe or have lower brightness, a 150 ohm resistor could be used.
If you make your own LED strings or know the specs of the LED you are using, you can calculate the resistor value precisely using free online calculators, such as this one:
LED Resistor Calculator
Instead of a resistor you can also use special current limiting components, Hansen Hobbies has them in 10mA and 20mA ratings. Unlike resistors which need different values for different LEDs, these restrict current flow to a fixed amount no matter what your LED rating is. If you want to use one of these, just wire it inline with your LED wire leads and jumper across the limiting resistor spot on the board. If you can't buy from Hansen Hobbies, the components are manufactured by Diodes Inc and the series number is AL5809.