Best interface to read voltage signal on PC?
One problem with trying to measure the pulses with microsecond accuracy directly over USB is that there will be delays in the USB stack and no popular desktop operating systems are real-time. Apart from latency the delays won't be consistent so you'll introduce jitter into the measurements as well.

A better approach would be a microcontroller that can record the timestamps internally and then send those timestamps over the USB port. There are a few ways to do that and it could be done with an 8 bit micro and some clever programming, but it is complicated by the fact that most only have 16-bit timers and clock rates around 20MHz or so. For a one-off project I'd recommend looking at something 32-bit like an ARM.

I haven't used one myself but the Arduino Due is one example and the Arduino boards in general tend to have a lot of example code and tutorials floating around. The library contains a micros() function that returns the number of microseconds the program has been running so you could record the delta between values (although be aware it wraps around). To detect the edge you could use the attachInterrupt() function to call an interrupt service routine on the rising edge of the signal.

On the interfacing side you could connect to any of the I/O pins listed as being an external interrupt. The board runs at 3.3V so it's important not to apply a voltage higher than that to avoid damage. In your case a pair of 10K resistors configured as a voltage divider would give 3.1V which is enough to be read as a high and gives you some safety margin for tolerances.