A few hints, FlipFlopDude-
Assuming you are in the U.S. and covered by NFPA-70
A) Article 422.11(A) requires the circuit's overcurrent protective device not to exceed the rating plate. Both appliances are considered Motor Loads, so the following apply.
I certainly would check the rating plate for circuit ampacity. The circuit can not exceed the maximum on either plate. Appliances with motor will have this listed on the plate so you are able to follow the rules in 1110.3(B), 430.6(A), 430.22 and a bunch-o-bunch of other places.
What this means is that if the dishwasher says 15 amps maximum circuit and both machines added up need 16 amps to operate simultaneously, you are not allowed to install a 20 amp circuit. For a friend, I wired for a Bosch energy efficient dishwasher which stated 15 amp maximum circuit.
B) Look at the Full Load Current rating of the appliances. If it seems that a 20 amp circuit will work and you install a 20 amp circuit, but use one receptacle outlet for both devices make sure it is a 20 amp receptacle outlet. When one outlet is on a circuit, it has to be rated for the circuit ampacity.
(You would be splitting the duplex receptacle. Oe side is aways live (dishwasher) and one side is live by the wall switch (disposer))
C) Since you are running new cable anyway-
Consider running 12-3 NM or 12-3 MC instead of 12-2. Now you can separate the circuits & share the neutral. This covers your bases. Be certain that the circuit breakers into which you tap are on separate phases, are adjacent and that you can use a handle tie across them.
D) Absolutely check the ampacity plates or manufacturer's information for the new appliances. Some dishwashers require as low as 8 amps with the heater on. (Can't remember which ones, Happen to notice this while dishwasher shopping for home a few months ago.)
E) Unless things have changed since my last code update class, neither a residential dishwasher nor a residential garbage disposer are considered Continuous Loads. There is no need for the hard and fast 125% rule. You will have to look up 430.22(E) and compare the chart with the ampacity rating of the appliances to determine the circuit amapacity. (Motor loads are complex enough that NFPA-70 has an entire chapter for motors.)
F)The cord for the dishwasher (if plugged in) has to be no less than 36" and no more than 6 feet 6 inches. It has to be in the space next to the appliance. Of course, both cords have to be protected against physical damage.
Complicated Rules? Yes.
If you would like to do the project yourself, and there is no reason that you shouldn't, it would be very wise to obtain a Homeowner's Permit from your city. Then take your information to the inspector, saying "This is what the appliance tags say" "This is how I plan to wire it" "This is the wire size and the breaker or fuse size". Does it look OK?
When the job is done, bring the inspector back for a check and Green Tag. This will cover you should there ever be a fire or injury. Your insurance company can;t wiggle out.
And, finally, if this is a rental or you do not own the property- Don't do the job. Get written permission from the owner and hire it out to a licensed and insured electrician with a permit.
I hope this helps and does not confuse too much,
Paul