So the question is ..... if I want the picture to look the same across as many applications, websites as possible should I just always use sRGB ?
Simple answer: yes.
More complicated answer: Yes, because...
...your picture existing as a digital file is just a sequence of numbers. To make an image out of these numbers requires a
mapping, a function or a table which tells you which number corresponds to which color. This mapping is known as a color profile or, in some cases, as a color space.
For example, sRGB is one color space. AdobeRGB is a different color space. The same numbers correspond to different colors in these two spaces.
In fact, displaying your picture on a screen is even more complicated. First, some software has to decide which colors do the numbers in the file correspond to. But then, these colors must also be displayed be the screen and it's a separate issue because (a) you need to know which numbers to send to the screen to make it display the colors you want; and (b) the screen is limited in which colors it can display (that's called its
gamut) and if you want to show a color the screen is not capable of, something must be done about it.
Generally speaking, sRGB is the right color space to use if you don't know on which device your picture will be seen. That is because it's the most widespread color space and it also the default color profile for most (non-professional) screens.
Do note, that different screens really differ in how they display color. You -- who publishes the image -- cannot control that. On some screens your picture will show up as too blue, on others as too yellow, on yet others as too dark or too bright and washed out... You can't do anything about that. People are not running color-calibrated monitors and that's just a fact of life.
If you want to delve further into this messy subject, google up "color management".
Real World Color Management by Bruce Fraser is a good book.