Hotch would feel a great sense of responsibility. He's the leader, and Reid getting hurt might make him question his decisions that led to the situation. He'd be very protective and focused on getting Reid back to full health.
Morgan would be angry, especially if Reid was hurt because of someone's negligence or malicious intent. He'd be determined to find out who was responsible and make sure they face justice, all while being by Reid's side to support him through his recovery.
One common theme is Reid's vulnerability. Fans often explore how his intelligence and unique personality can make him a target in different ways. For instance, in some fics, his prodigious memory might be used against him, leading to his emotional or physical hurt.
Some fanfictions might also focus on the mystery or the circumstances surrounding Reid's injury. It could be related to a case they were working on, and the story delves into how the team tries to solve the mystery of who hurt Reid and why, all while dealing with the fact that he's injured.
One common theme is the team's unity. When Reid gets shot, the team comes together, showing their strong bond. They support each other and are determined to find out who hurt Reid.
The other BAU members would be devastated. Reid, for example, would be extremely worried. He has a close bond with both of them, especially Penelope as they often share their geeky interests. He would probably blame himself for not being able to predict the situation. Hotch would feel responsible as the team leader. He would be very focused on finding the culprits and getting them to justice. Morgan would be angry and determined to rescue them. He would see it as his duty to protect his friends. Emily would be concerned but also try to keep the team together and focused on the investigation.
One scenario could be that Reid gets hurt during a chase. Maybe he trips and falls while running after an unsub, and sprains his ankle. This would slow him down and make him vulnerable.
The whole team would experience a range of emotions. JJ would be concerned not only for Morgan but also for how the team is handling it. She might be the one to try and comfort Garcia. Prentiss would be angry. Angry at the shooter and also at the situation. She would be determined to bring the person to justice. As for Morgan himself, he could be feeling a mix of pain, fear, and determination not to let this be the end. He would be thinking about how he can get back to the team as soon as possible.
One great place to find Criminal Minds Hurt Reid fanfiction is Archive of Our Own (AO3). There are numerous stories there. For example, 'Fractured' which delves deep into Reid's emotional turmoil after a particularly harrowing case. It really captures his vulnerability and the team's reaction to his pain.
They'll likely interview people who had recent contact with Reid. The team will also analyze any communication from the kidnapper if there is any. Based on their profiling skills, they'll narrow down the suspects and search for the location where Reid is being held. Morgan might use his combat skills and Garcia will be crucial in providing technological support to find Reid.
Vivi would likely feel a great deal of guilt. She might blame herself for putting Luffy in harm's way. After all, he got hurt because of her. This guilt could drive her to be more proactive in helping him recover.
Twilight Sparkle would likely be extremely worried. Since she raised Spike, she would feel a deep sense of guilt, as if she failed to protect him. She might even blame herself for putting Spike in a situation where he could get hurt in the first place. She would probably rush to find a way to heal him, using all of her magic knowledge.