and good luck with your circuit adventures !
i think AVEMOD would be a great place to start building some video circuits. from what i understand the VISUALIST is more complex and needs some harder to find parts, so i would recommend getting familiar with some smaller/easier projects before trying that one.
im guessing you are intending to build these on a strip/breadboard from the schematics ?
another (easier) option is to grab a pcb (then all the traces are already connected , you only need to think about placing components )
but if you want to build from the schematics, then yes multiple ground / power source symbols is just a short hand way of saying all these things are connected together
so in this schematic every part where it says GND should be connected, and same with every part it says +12V
so with this in mind you can see that even parts of the schematic that look disconnected actually are connected through these label shorthands.
some schematics use labels for other parts of the circuit too in an effort to make them easier to read. heres a version of the avemod circuit i was working as an example (debatable if its actually easier to read 
):
and ofcourse maybe @BastienL might have something to add 