I guess not my triumph since the speedo is analog.
If this is a fairly new Triumph I would expect the speedo to have an electronic pick-up. An old one will for sure have a mechanical pick-up at the front wheel.
I'm looking at the rear sprocket to mount the magnet with a switch or sensor on the swingarm or chain guard. The front sprocket is another thought for the sensor though. It would shorten the wiring be solidly located and under cover. It could be doing 50-75 revs per second so a divider might be needed there too.
The hall sensor you posted a picture of would give a clean signal, and I don't see any problems in hooking this up to one of the external interrupt pins on the Arduino. In the interrupt handler you store the time since the last interrupt in an array, and whenever you need to know the current speed you use the average time between interrupts to calculate speed.
What will your display look like?
That is not decided yet. I have a graphical LCD display (KS0108) that I'll use, but I have not decided how the GUI should look like yet.