>>31066513some are connected. the manga covers the whole main series (and ranger, plus a cameo of snap). The remakes and the 'third' game is always connected to the original and first two games respectively, but in each generation there's some degree of independence.
PokeSpe imagines there to be one bug world, so events happening in one generation can be referenced in another. This happens often.
In detail:
RBG is the first arc, so no worries.
Y follows from RBG and has the same protags
GS is independent, but doesn't end and continue into Crystal, which had all the protags of RBGY.
RS is self-contained
FRLG of course features protag of RBGY and GSC
Emerald continues from FRLG and had all the protags from RBGY forward at the end
DP is self-contained, although its ending continues directly into Platinum.
HGSS mostly sticks with GSC characters, but of course refers to events in GSC
BW is self-contained
B2W2 is a direct sequel to BW
ORAS refers to RS events and they have RBG characters
XY is mostly self-contained, but later they have a RBG character
SM only just started
it's not super continuity focused for the most part, though, so choose your fav gen and start with the arc that covers the first games of that gen.
