I am good at fighting so I would like to use fuseki that encourages fighting.
You can fight in any fuseki, though some lend themselves to that more than others. When you’re talking about fuseki that invite and/or favor fighting, you’re really talking about having large-scale frameworks. The reason is straightforward. If you are claiming more territory than your opponent, your opponent is of course going to come in to prevent such a foundation from being built. You will also be drawn to fusekis that emphasize influence (good for fighting) over building territory. With these in mind, I have some recommendations:
Kobayashi opening: Kobayashi is a common opening formation playable by black or white in which the player sets up a big framework and invites invasion or approach.
Opposing 3-4: If black plays for Orthodox or Mini-Chinese, oppose it with your own 3-4 point. The purpose is twofold: disrupt your opponent’s opening theory, and invite them to make a large-scale framework even if it’s not their style to do that. Then you get to invade and start fighting.
You can find all of these in recent pro games, so they can’t be bad. Hope you find something good!!
If fighting is your goal, then pick a fuseki designed around building a moyo. By its nature, a moyo will eventually need to be invaded or reduced in order for the game to end in the other player’s favor, so set up your framework and wait to try to profit from the aggression. Mark above recommended the chinese and kobayashi fusekis, which are both designed around this very concept, and I highly second them
If you’d prefer to be the one who initiates battle, rather than inviting it, then a more “grab the money and run” style may be more for you. Playing for solid profit, then being aggressive toward your opponent in order to prevent him from developing faster than you.
Modern pros tend to favor profit over moyo in their openings, and the recent meijin title match actually had quite a few games where being aggressive after playing for points factored heavily into Iyama’s victories
Mark5000 and Kitten1 said most of it, I would just add, that father and grandfather of Chinese, Kobayashi etc fuseki family are San-Ren-Sei and Ni-Ren-Sei and if you are recently starting your adventure with go, those two would be suitable for you since they are in certain sense simplier to learn than their more complicated descendants. Characteristics are same: fast development, influential play, framework moyo.
Are there any fuseki that do not encourage fighting?
Plop a stone in the middle of the board and try to kill something.
Probably Orthodox is the calmest opening, although there can be difficult fighting in that, too. The key to a peaceful game is accurate counting where you take barely 51% of the board. This puts your opponent in the dubious position of invading a pretty solid position or just taking a big point, which won’t be enough if you counted right.