Before I start, I remind you that this is only my opinion. You don't have to agree with it if you don't want.
So, let's start at the very beginning. If you don't know yet what kind of game do you want to make, think that first. Think about the storyline, at least how everything begins. Then, if you haven't made it up yet, choose which type the game is. I'll put here a couple of examples:
RPG = Role Playing Game
I myself like pretty much RPGs. In RPG You control the hero and his/her friends. Usually there is always some kind of evil or mad guy who wants to take over/destroy the world. Of course your hero won't accept that and will fight against all the bad guys. Pretty often there is some journey in the game. RPG is pretty often made somewhat Fantasy - style so you can use a lot of imagination when making this. Of course there are other style RPGs as well, I have even found a couple of Scifi RPGs! Most of RPGs have a level system. That means that when your hero kills bad guys, s/he will gain experience points. When you get enough points, your hero will gain a level and grow stronger that way!
RPG's battle styles are usually based on turns. Normal battle starts randomly when you walk around. You will be teleported to battle screen. In basic turn based battle system you will choose in order what will your characters do. When you have chosen everything, the fastest one will attack first. When everybody, including enemy has attacked, you will choose your characters actions again. This will continue as long as you defeat the enemy, you die or you run away. There is more versions of this style, example ATB (Active Time Battle) where everything is the same exept you don't choose your characters actions at the same time, you have to wait for your character's ATB meter to fill up, then you can choose the action. This style is more speedy, you don't have all the time to choose the actions because the enemy can attack you when you are choosing your action. There are still tons of more RPG battle styles but I'll leave that searching for you...
There is a lot of internet RPGs too. They are usually called MMORPG. (Massive Multiplayer Online Role Playing
Game)
Some pics:
MMORPG game


Well that's enough for RPG...
Then there's the basic War games! I don't have so much to tell you about this, because I think everyone knows the idea of gun games: Shoot 'em down!
Well, if you are doing your own game this will be really hard to make it look good, especially if you were thinking of 3d version. Well, everything's possible if you have program powerful enough especially for making shooting games. If you really are making a 3d gun game, you need to choose are you going to make it 1st person view (you only see the gun of your character) or 3rd person view (you can completely see your character). I haven't ever made a gun game, mostly I do RPGs or fighting games so I can't help you much about this... If you are going to do a shooting game, pack a lot of action in it!
Pic:

1st person view
Then there's fighting games. Usually they are viewed on the side of players (usually your character is at left side of the screen and the enemy (player 2 or CPU) is at right side). Such as Tekken, fighting games are made usually only for fighting. I tried to make a RPG fighting game, where you could move on the map and sometimes you had to fight other dudes. This worked out suprisingly well (I know, I didn't explain it properly but I hope you got the picture...). My opinion on fightin games is that I like them, but in the end they start to be little boring because it's always just that fighting... Well this may be because I can't play very well them, I always only hit all the buttons at the same time. :)
Pics:



Well, I haven't ever played this...
Of course there is plenty of other game types but as I said, I put only a couple of games here so if you are looking of another kind of game, you have to look for yourself...
Well, when you have desinged the beginning of the game, you know what kind of game type it will be and you have good game maker program to fulfill your plans and you can use the program well enough, you are ready to go!