OpenGL - Trouble with first person camera matrix

I have tried my best to create a camera that mimics the style of a first person camera. I have just switched from the old OpenGL method of rendering and am now ready to tackle a camera matrix. Here is my code for my camera update.

void Camera::update(float dt)
{
// Get the distance the camera has moved
float distance = dt * walkSpeed;

// Get the current mouse position
mousePos = mouse->getPosition();

// Translate the change to yaw and pitch
angleYaw -= ((float)mousePos.x-400.0f)*lookSpeed/40;
anglePitch -= ((float)mousePos.y-300.0f)*lookSpeed/40;

// Clamp the camera to a max/min viewing pitch
if(anglePitch > 90.0f)
    anglePitch = 90.0f;

if(anglePitch < -90.0f)
    anglePitch = -90.0f;

// Reset the mouse position
mouse->setPosition(mouseReset);

// Check for movement events
sf::Event event;
while (window->pollEvent(event))
{

    // Calculate the x, y and z values of any movement
    if (event.type == sf::Event::KeyPressed && event.key.code == sf::Keyboard::W)
    {
        position.x -= (float)sin(angleYaw*M_PI/180)*distance*25;
        position.z += (float)cos(angleYaw*M_PI/180)*distance*25;
        position.y += (float)sin(anglePitch * M_PI / 180) * distance * 25;
        angleYaw = 10.0;
    }
    if (event.type == sf::Event::KeyPressed && event.key.code == sf::Keyboard::S)
    {
        position.x += (float)sin(angleYaw*M_PI/180)*distance*25;
        position.z -= (float)cos(angleYaw*M_PI/180)*distance*25;
        position.y -= (float)sin(anglePitch * M_PI / 180) * distance * 25;
    }
    if (event.type == sf::Event::KeyPressed && event.key.code == sf::Keyboard::R)
    {
        position.x += (float)cos(angleYaw*M_PI/180)*distance*25;
        position.z += (float)sin(angleYaw*M_PI/180)*distance*25;
    }
    if (event.type == sf::Event::KeyPressed && event.key.code == sf::Keyboard::A)
    {
        position.x -= (float)cos(angleYaw*M_PI/180)*distance*25;
        position.z -= (float)sin(angleYaw*M_PI/180)*distance*25;
    }
}

// Update our camera matrix
camMatrix = glm::translate(glm::mat4(1.0f), glm::vec3(-position.x, -position.z, -position.y));
camMatrix = glm::rotate(camMatrix, angleYaw, glm::vec3(0, 1, 0));
camMatrix = glm::rotate(camMatrix, anglePitch, glm::vec3(1, 0, 0));
}

The last 3 lines are what I assumed would update the camera with the opposite of the translation (y, and z switched for the format I am working with). Did I do them in the wrong order?

Here is my very simple shader:

#version 120

attribute vec4 position;
uniform mat4 camera;

void main()
{
    gl_Position = position * camera;
}

#version 120
void main(void)
{
    gl_FragColor = vec4(1.0, 0.0, 0.0, 1.0);
}

This simply makes a red triangle. The camera sort of rotates around the triangle, which is not what I want. I want it to rotate the camera. I thought multiplying a camera matrix by each vertex would give the rendering in camera space. Or do I need to multiply it by the projection matrix as well?

Moving w, a, s, or d zooms in really close all at once and distorts the whole view with red fragments everywhere.

Write your matrix operations in reverse order. So if you want to translate (to camera position) and then rotate, write it in this order:

// Update our camera matrix
camMatrix = glm::rotate(glm::mat4(1.0f), anglePitch, glm::vec3(1, 0, 0));
camMatrix = glm::rotate(camMatrix, angleYaw, glm::vec3(0, 1, 0));
camMatrix = glm::translate(camMatrix, glm::vec3(-position.x, -position.z, -position.y));