I noticed than the Standard preset of colors of my monitor produce more vivid colors than Adobe RGB preset. As far as I know, the monitor can reproduce both sRGB and Adobe RGB. Thought that the Adobe RGB should be the wider gamut that the monitor could reproduce.
I also noticed that Adobe RGB preset look brigther than the standard one
Could someone clarify that to me?
It's hard to say what the 'Standard' setting is supposed to do on each particular monitor. From my experience with similar monitors, where there are 'actually standard' presets like sRGB or AdobeRGB and then some others, the Default or Standard preset can be one of two things:
The first one is preferable (unless there is a special Native or User setting): you can use it for your own calibration (with a colorimeter). The latter is more common, and from what you are describing, yours is like that. No wonder 'best looking' for a typical consumer means oversaturated.
It is common for people doing their first colour calibration to complain that the calibration made things 'worse': duller colours, yellow cast, etc. But one should remember that the point of calibration (or standard presets, i.e. factory calibration) is not to make display 'better' (in a common sense), but rather to make it accurate and consistent.
There is one more thing. According to specs, your monitor is a wide gamut one (99% AdobeRGB). Such monitors require colour management: most content you find was (and still is being) created for sRGB*. If you view a 'normal' (sRGB) photo on your monitor (in it's native setting) without doing anything, it will appear oversaturated and (likely) with some magenta cast. So there are three ways you can (and should) approach this situation.
I can't stress the importance of correct software setting enough. Without it (unless you follow the first approach), everything will certainly look wrong, and you would be better off with a cheaper standard monitor. You need to make your software aware of the capabilities of your monitor (remember they are not the most common ones!) by selecting the appropriate colour profile. This also applies if you change the preset on your monitor: by doing that, you effectively change your monitor!
The good news is that in most cases it is enough to set the OS right, and the applications will use this setting. But still, some software disregard the OS settings and have their own, while some just don't colour manage. Some do manage, but only if the image has an explicitly attached profile. It's hard to be sure, esp. on Windows, and you need to check and trust each app to do the right thing. There is still no common mindset that colour management absolutely must be done. (Mac is much better in this regard, but I can't say if it's perfect).
As for brightness, this is (theoretically) an independent setting from colours. You can have, say, AdobeRGB at different brightness levels. However, in practice changing the brightness may shift colours a bit; this is why proper colour calibration (including factory presets) includes brightness and contrast in its target, and once calibrated, fixes them. But if you find your AdobeRGB preset brightness uncomfortable, you have no choice but to manually adjust it and hope the distortion will be negligible. This is if your monitor even allows you to change brightness for such preset: many professional monitors simply don't, and you need to re-calibrate for each brightness.
(*) Or rather, more often than not without any colour management, but on a sRGB-like equipment.
You have to be careful that the monitor settings match the color space that your software is trying to display. If the software is configured for Adobe RGB but the display is sRGB, it will look muted. If the software is set to sRGB but the display is Adobe RGB, the colors will be overly vibrant.
This is because the overall color space gamut will be encoded into the same range of numbers, typically 0-255. In Adobe RGB 255 will be a much more intense color than 255 in sRGB, simply because sRGB doesn't need to reach as far.
