Now that you’ve had a look at your new territories, it’s time to take a gander at the new places that have opened up. From lowest to highest power, you have Cragspur, Viperia, Yaksha, and Avia. Cragspur, with a power of 1300 waiting in it, is a Rock-oriented region, though one of the defenders there has a Machop and another has a Pansear- both of which can do some noteworthy damage to things that you would otherwise love to bring in against the Rock-types.
More-distant, Viperia is the area for Poison pokemon for hte most part, as demonstrated by Ekans, Arbok, Zubat and Golbat being present among the defenders. Spiritomb will throw you for a loop, though, being immune to the Psychic types you would usually use here. Still more interesting, this area contains three major opponents, including a matured Hideyoshi (see the moustache?) Who has apparently evolved his Chimchar since you last saw him. He also provides a solid fifth of the might in this area.
Yaksha is clearly Dark-aligned and thus would normally make a great place for Fighting and Bug pokemon, but the presence of a Scraggy, a Scrafty, and a Zubat all threaten Bugs, and that Zubat’s Wing Attack can really cripple Fighting pokemon. Zoroark also promises to be a bit of a challenge, as it’s always been a bit of a stumbling block in every game it appears in.
Finally there is Avia, home of Flying-types only. Again there’s a bit of a twist, as the secondary fighter there uses a Carnivine which will not care as much about the Electric attacks that will wreck most everything else present- fortunately, nobody thought to bring a Skarmory, Aerodactyl, or anything else of the sort, so a few good Rock attacks will likely flatten the opposition when you get there.
I’m going to assume you’re going in the sensible order, from weakest to strongest, and thus we’ll be covering Cragspur first of all. This being the rocky place that it is and one of the major defenders using a Fire-type, you’re definitely going to want to bring some Water and Ground attacks to bear. In fact, there’s little reason for anything else if you can get together an entire assault force between those two types- Ground/Rock pokemon may need to watch out for Machop, as will anything Water/Ice (Spheal), but that’s about it. Empoleon is weak to Fighting attacks, but if you have one already its power is likely to be so far beyond Machop’s that you’re just not going to care.
You can bring in some Grass-types if you like, just be sharply aware of where that Pansear is, because it will utterly destroy them if it gets a direct hit with its Flame Burst.