Help on moiré and noise on videos

[amsportdesign]

HI there,
I am new to videography with DSLR, I just bought a 700d to get myself on the learning track with both photos and videos.
Basically yesterday I went outside (as my aim is to make sports videos and travels) with the standard 18-55 lens aiming to try and learn the settings of my camera
After watching some tutorials I set up the camera as PAL 1920 x1080 25 fps / 1/50 / ISO 100 in sunny daylight. On camera was kind of ok, but once watched on my computer I noticed I was getting a lot of noise in my shadows, plus things like foliage, tiles, bricks, railings or any detailed pattern around were getting lots of moiré / aliasing effects.
I then noticed that these effects were less with a wide focal length, more with a closer one.

Following some tutorial suggestions I lowered the shutter speed to 1/40 and then to 1/30, then I went to set my picture scene to neutral and I lowered the sharpening at 0, same for contrast. Then I lowered just a bit the colors and saturation trying to obtain the flattest scene possible. As of the last thing I did put my WB in "sun" preset. The whole thing solved almost completely the moiré and but unfortunately, I could still see some aliasing here and there where the sun was hitting harder on roof or bricks in the background. The noise instead was still there in my shadow.

So I went testing the same scene with different f-stop (from 3.5 to 22) at different ISO (from 100 to 400) and even if it solved a bit at certain combinations, the noise and the aliasing were pretty much always there more or less.

Last thing last I repeated the whole test with my 50mm 1.8 and even if it was better, still was not smooth as it should be in my opinion.

Now, the questions I have are:
Is there anything I am missing, doing wrong?
Having the shutter speed that low could be a problem on fast moving (sports) scene / fast panning? If yes how can I address the issue without getting back the moiré / aliasing effect?
Are there any kind of antialiasing filters to help to solve the issue?
What can I do to reduce noise at maximum with my camera?

Anything you can suggest will be really appreciated, I would like to get the best out of this camera before considering anything different. Thanks a lot to anyone that will take the time to reply to this long post. 

[Waddizzle]

I use this link frequently to select lenses.  The content at this link has not changed in the last few years.  

http://www.dofmaster.com/doftable.html

You may want to take note of the hyperfocal distance.  I like to use a manual focus 14mm lens as a walk around lens. I dial in the hyperfocal distance, and everything beyond a couple of feet is razor sharp.  I do not need to refocus it for every shot, just check it to see of the focus ring has accidentally turned.

[BurnUnit]

Now you're getting somewhere! Looks like you're starting to get a handle on things. The lighting in your sample clip looks to be much more concentrated toward the middle of the histogram. The camera isn't having to struggle to resolve detail (possibly unwanted) in a lot of bright highlights or deep shadows.

There's a couple of areas that look slightly underexposed to me but I'm guessing that's just part of the cinema profile that you've installed. That and the fact that I'm looking at the clip without of any sort of context.

Good catch too on reducing or turning off any in-camera sharpening.