I just finished building the Tamiya 1/16 scale King Tiger, and recommend a primer coat for most parts. Primer adds "tooth" to the parts, which allows the paint to adhere more firmly to the parts. Also, sometimes a coat of primer makes surface defects that you've missed more visible.
I usually give a model a light sand with 600-800 to get rid of mold parting lines and to "roughen" up the surface a little so the paint will have more "tooth" or surface area to cling to - it makes the paint stick better and can prevent paint flaking off a model.
Use as light a colored primer as you can for things like cars, as (for example) putting red top coat (on a car) over dark grey primer would need about a thousand coats of red to get a full deep color; whereas if you primed the car with flat white, you'd only need the "normal" number of coats to get a rich deep red.
For the King Kiger, I used a mid gray primer, then flat black was sprayed along all the panel lines and recesses. When I started with the color coats, I thinned the paint a bit and now the panel lines kind of stand out because they have a darker color on them. Get it?
You certainly don't need to prime for EACH new color, just the once.
I use a lot of different paints to prime - it just depends on what kind of paint I plan on using on the model.
I use automotive acrylic on some things like airliners and some cars- it dries fast and sands and polishes within a few hours of application. Apply sparingly as the thinner in the paint is "hot" and etches styrene, too much can warp your model (I'm not kidding).
Model Master makes great enamel paint - they've got a lot of greys you can use, and Tamiya acrylic is also very good.
As a base rule, until you gain experience in what damaage one type of paint can do to another (enamel over acrylic for example) it's best to use the same type of paint for priming and topcoats.
When in doubt, EXPERIMENT. It's easier and cheaper than finding out too late that a type of paint eats another.
Have fun!!
Lee Tree