I shoot in "P" mode with dial-spins to drop into Av or Tv as the need requires... Av much more than Tv. M generally only for tripod shooting. Usually, I am moving too fast for "M" mode (and I am quite comfortable with it, having been using full-manual film SLRs for 20 years.) If I need the specific unchanging control of exposure that M gives you, I'll usually just lock the exposure when it's where I want it. If I want specific control of both aperture and shutter speed, I'll use TAv mode; I rarely do though I could see myself moving towards that in the future. More explanations at the bottom of this message.
I find that in full Auto my shutter speed is never correct in low light situations resulting in blurry pictures. A photographer friend suggested I move to TV and last night was my 1st successful shoot in the school gym. I am over the moon that I finally got some good pictures.
I could pull out my manual but it's easier to just ask you. Do you mind telling me what I have control over in P mode?
Another question for you since you use a K-X. How do you know you are focused on the right location with the lack of LED focus confirmation? I've been told to focus on the eyes as much as possible but find that difficult without visual confirmation.
Thanks for always being patient with me. I'm learning just not fast enough. LOL.
Some good news for you: on the Pentax, it's probably easier and faster to do what you want than on just about anything else out there. It's because Program mode is very flexible - in fact, it's called
Hyperprogram mode.

(Side note: I've found that the modern Pentaxes tend to favor a slightly slow shutter speed out of the box, due to the in-camera shake reduction - for static objects, you can get away with a slower shutter speed than you think, but that obviously doesn't help for action shots!)
Here's what you do: Just spin the dial! Out of the box, the K-x is set so that spinning the dial will do a "Program Shift" - which means that it will adjust the aperture, shutter, and ISO. Spin it to the left, and you'll get faster shutter speeds and larger apertures. Spin it to the right, and you'll get slower shutter speeds and smaller apertures. Press the Green button to return to the "normal" program line.
If you want true "Hyperprogram" mode, go into the Menu and find the Green button settings. In there, you can change the dial to adjust the Program Shift, Av, Tv, or to do nothing. If you find yourself wanting to specifically adjust shutter speed mode, set it to Tv. By doing that, the camera will drop into Tv mode as soon as you spin the dial. When you want to go back to Program mode, just press the Green button. This means you can easily do this while your eye is up to the viewfinder; it will be second nature after you've done it a few times.
Hyperprogram is why I rarely leave P mode. With the front and rear dials on the higher-model cameras, one dial immediately drops you into Av and one drops you into Tv. You can switch between then at any time, and the Green button brings you back.
In addition, you can set your "Program Line", and bias Program towards action (fast shutter speed), two kinds of DoF (small or large aperture), MTF (the sharpest aperture as recorded in lab tests, obviously it only works properly with OEM lenses that are in the camera's database!), normal, or Auto. I usually keep mine on "action", since I'm often taking kid photos and need that faster shutter speed. In addition, you can configure how Auto ISO behaves, ie how eager it is to just to a higher ISO level. With all these settings, you can generally make Program behave like you want it to without needing to worry too much about specific settings.