If we were to divide Pokemon Adventures into "arcs", then we could basically do that by series of video games.
Red and Blue
Gold, Silver, and Crystal
Ruby and Sapphire
FireRed and LeafGreen
Diamond and Pearl (not yet published in English)
Since Pokemon Adventures does more or less follow the pattern of the video games, dividing the series into these arcs is appropriate. So, to summarize briefly.
Red and Blue follow the games closely. Red(essentially Ash in the anime) follows the standard path of a trainer through Kanto, interspersed with meetings with Team Rocket and gym leaders as it is in the game. Changes from the games include the use of several Gym Leaders as members of Team Rocket in addition to giving greater depth to various characters and changing the way the Elite Four/Indigo Plateau operates. Red and Blue (Blue is named as Green in the japanese translations of Pokemon Adventures but English translations have him called Blue. Due to a mistranslation in Volume 25, I'm going to refer to him as Green in the downloads) centers mostly on the three starter trainers and their adventures culminating in a decisive battle for supremacy in Saffron City (Volume 3) as well as the Pokemon League Championship match between Red and Green.
Yellow begins with Volume 4 and centers on Yellow as a character. This arc occurs two years after the first arc. Yellow possesses unique telepathic and telekinetic abilities because of her birth near the Viridian Forest and is instrumental in the search for Red, who has gone missing. The Yellow arc sees the introduction of the Elite Four, who are evil in the manga and a significant force. Yellow as an arc sees some truly awesome pokemon battles and really brings Pokemon Adventures into its own as a manga.
Gold, Silver, and Crystal do not see any real separation between Gold and Silver and then Crystal as we did with the first two arcs. GSC is one arc, though Crystal as a character is introduced later then Gold and Silver. The third arc occurs about a year after the Yellow arc, and therefore three years after R&B. One major change between the games and the manga is the introduction of a new leader for Team Rocket. In the games, Team Rocket is led just by some executives who try to get Giovanni to come back. In the manga The Mask of Ice is introduced as the new leader of Team Rocket. The Mask of Ice is also a gym leader and has significant amount of background which is covered even through the FRLG manga. The arc culminates in a battle to stop the Mask of Ice from obtaining Celebi. While the GS ball is shattered and Celebi freed, the Mask of Ice is lost in time.
Ruby and Sapphire bring the manga to a new beginning with Ruby and Sapphire as pokemon trainers. Professor Oak is in this arc, but the old trainers from RBYGSC are really only mentioned in passing. The Ruby and Sapphire arc centers on the fight between Aqua and Magma as well as the competition between Ruby and Sapphire (contests vs. gyms) and results in the apocalyptic battle between Groudon and Kyogre as well as Ruby revealing his powerful abilities as a trainer. This arc, I believe, takes place another year after the GSC arc. I've been searching through my copies of the manga for confirmation of that, but have yet to find anything specific.
FireRed and LeafGreen takes place another six months following the conclusion of events in the fourth arc. We are brought back to Red, Green, and Blue who are about to meet up with Blue's parents as well as explore the Sevii Islands. The fifth arc re-introduces Giovanni as well as Team Rocket as a powerful force. Arguably, Team Rocket is stronger in FRLG than it has ever been before as Giovanni comes into possession of Deoxys and uses it to find his son. Furthermore, this arc introduces the trio of elemental attacks that are learned on Two Island in the games. The arc climaxes with a battle between Red and Giovanni; Red using Mewtwo and Giovanni using Deoxys. As has now been firmly established as a trademark of Pokemon Adventures, we get to see a truly awesome pokemon battle.
I'm going to list all of the characters in the manga. They'll be divided by tabs by which arc they were introduced and from there in alphabetical order.