`mute`is under the "TRUMPET/CORNET SURVIVAL KIT" catogory of my method book, but i dont really think so, and if it is, which mute should i buy?

You need 2 to survive, 4 to cover all bases.
1 straight
1 Harmon - wahwah du all

Optional (but my opinion is must have as well)
1 cup
1 Velvet lined/ or rubber wah-wah

what does straight and cup mean?

Straight is a cone with no curves. It delivers a sharp/clear sound but a little quieter and muffled.

Cup has a Hat on the end of the Straight mute. Some have a scalloped surround on the cup, others are just circular.

You can get some really great sound affects with mutes, and it helps a small bands with variety.

Big Bands have Cup and straight as usual, and the Wah-Wah is great for affects. There`s a whole world of sounds with mutes, and it really does make a diff...

what does each do?

and can u show me their pics

Hi,
The straight is probably most used. It is narrow, easily stored.

Sounds OK. Just place it into the horn and blow, it has usually 3 cork pieces (sometimes 4, but 3 is better) to hold it in place. Easy to get in and out. I have 2, 1 aluminium I use for practice, and 1 Humes & Berg. It is Red and White and looks good. A better sound as well. Good volume.

Cup Mute is cool, and more mellow. Also relatively good volume.

Wa-Wah Du All, is great, and probably most versatile. I usually wet the cork round section with my tongue and a slight screw pressure to get it into the horn. There is a central slider that does the Wa-Wah with your left hand (assuming right handed for valves) and this can also be moved out to various lengths to get a different base sound. Remove the centre, and it is Miles Davis style.. A great asset, and worth the extra bucks. Also a good practice mute.
Downside it takes up space, and a little slow to get in and out. If you don`t wet the cork it can also squeek when taken in and out. Pretty quiet, good affect with a Microphone.

Plunger/Wah Wah is great. You move it to get the sound affect. You can get the gutteral roar from the back of the throat, and also "Roll the Rs" with the tongue as you play. A really great affect, and draws huge attention. Great volume. Really good affect - get a coffee/tea cup off the nearest Table and use as a plunger...man does it sound good and get the audience up.

Put a Pixie mute in, and use a Rubber Plunger, and man what a sound. Completely different, and is excellent when you re-enter after a break - it gives a completely Black/White sound to the Plunger only. Volume not really great, the pixie muffles, so best to use with a mic.

I use nearly all Humes & Berg. My aluminium practice mute is unknown- I lost the name off it a couple of decades ago.

Try this link, and I suggest go into a good store and try them out, especially if you play a range of music for small bands. It does really assist to give a variety.
http://www.dillonmusic.com/departments/mutes.html

I am keen to hear any feed-back on better sounds out there, and useful effects with mutes....

for a one year trumpet player, which mute(s) should i buy first?

A straight Mute. Get good quality all the time, they keep in tune.

Then a Harmon. You will love the Harmon.

i cant find the Plunger/Wah-wah in the web

Think of a toilet Plunger - used to clear the toilet bowl. Now take off the handle, and that cup is the plunger.

Get a ceramic Coffee or Tea cup from Mum. Be sure it is not the best one.

Now place it in your left hand with the thumb through the holder.

Holding the trumpet, now stretch the left hand so the cup is over the bell.Take the cup to the bell, but do not fully touch the bell at all. leave a space. now tilt the cup out, and play a couple of notes...move it slow, and quick. you will get the idea

although i know what mutes i need, i still dont understand why i need mutes!!??

Usually you`d start with a Practice Mute. Why? because a beginner is torture to those around you. Ever listened to a beginner on violin or Piano.
You try to keep your mistakes to yourself, and you can let fly as loud as you like, and no-one else will hear you. Practice mutes, self explanatory.

Other mutes, well the music asks for it. Sometimes to quiten the Brass section to balance for a singer or soloist, or to get affects. The Music will say what mute to play with, or your Band leader will tell you.

You need to learn to blow with a mute, and understand how to get the best out of it. Would a Miles Davis signature tune sound the same without the right mute?