OK, here is an idea, although others are possible.
You are dealing with a low-frequency signal: 2500/2/60=20.833 Hz.
In fact, you should account for about 600rpm to 6000rpm, that is 5Hz to 50Hz. Multiplying the frequency by 2.88 you get the speed in mph.
For example, at 2500rpm, you get 1250 pulses per minute, that is 20.8333Hz. Multiplied by 2.88 you get 60, the correct speed in mph.
So you need to measure accurately this frequency, multiply by the constant and display the result. If the result is higher than x mph, do this or that.
You need to refresh the display several times per second. One method to measure low frequencies is to count the pulses over 10 seconds. Obviously, you cannot use this method, since the update rate would be too slow.
Another method to measure low frequencies with high resolution involves measuring the period of the signal and inverting it. f=1/T. This is the method I suggest you use, since you get update rates of 5 to 50 times/ sec. That is fast. You can reduce it to 2.5 to 25 times/ sec. This is what I am going to suggest, for other simplicity reasons.
So, the method I am proposing is this: amplify the signal, shape it into pulses and measure its period: use a high frequency stable oscillator (quartz controlled) and count its pulses between two rising or falling edges of your input signal. The easiest way to do this is to use a D FF and divide the input frequency by two. That way you get a HI between two similar edges. You can use that signal to enable an AND gate that feeds the pulses to a counter. This is how you measure the period.
Now for the calculation, it would be easy to use a micro. Since you cannot, use a trick: a lookup table. The outputs of your counter will address a couple of EPROMs. For each address combination, corresponding to the measured period, enter in the EPROM the actual speed, directly in BCD. Then all you have to do is use the EPROMs outputs to drive BCD/ 7seg decoders and you display the speed in mph. Not math, no nothing, just patience to calculate all those speeds and program the EPROM's.
Since you only need 12 bits for your 3 digits, you can use the remainig 4 bits to implement the alarms: when the displayed speed is between 60 and 69.9mph, have one bit HI, between 70 and 79.9 another and over 80 yet another. Then use these bits to enable some oscillators that will produce the required frequencies (you can use some frequencies derived from the same crystal oscillator, just divide it down to whatever is needed, then enable some gates using those extra bits of the EPROMs and you have the sound, too).
Note that you should use some D- latches (74x174, for ex) between the EPROMs outputs and the BCD/ 7 seg decoders. These will be reloaded every time a new result is available. This will prevent glitches. You will need to develop some logic or simply use one-shots to take care of the timing.
(If you want to get fancy, use a fourth 7-seg display and a switch to change some addresses on the EPROMs. With that, you can build a 4-digit tachometer, so you have a dual function).
I hope these suggestions help. Please post if you need more help.