Most designs are based on high bandwidth op-amps wired up for whatever the necessary voltage gain. TI, National, and Maxim make good options. I've used the TO OPA3692 with good results, but I'm not sure if that part is available in through-hole.
Check out the TI OPA350 (you'll need 3 - one for each channel). You can just wire it up as a standard non-inverting amp with whatever gain you select. TI will give you samples. As this is a fairly high-speed circuit, it's a very good idea to place quality bypass capacitors near the power supplies for each chip. There should be (at minimum) a 0.1uF ceramic very close to each chip's power supply pins, a 1uF ceramic somewhere on the board near the chips, and a largeish (10-100uF) bulk cap near the power supply into to the board.
A gain of 2-2.5 is about right if you have a relatively high impedance input (~1k ohm recommended) from your PC (which results in ~1.4Vpp signals). If you properly terminate the inputs from the PC into 75 ohms (recommended for best quality, but probably not really necessary with 15kHz timings), you'd need a gain of double that (so about 4-5).
If the amplifier oscillates, try placing a small resistor (~10-100 ohms) between the output of the amplifier and the wire running up to your monitor. Also check your bypass capacitors or add more (smallest ones closest to the pins then getting larger as you move away).
Building this on a solderless breadboard may give mixed results. The parasitics on them are pretty bad. A solder based perfboard is recommended.