Poison seems like a good type to start off with (it isn't overpowered or anything) plus I think we have a lack off Poison gyms.
Ground after seeing the deserty area it reminded me a little of the Virbank Complex plus Europe is quite hilly so ground seems like a good choice and again we've had a few early ground types in the past Sandshrew, Geodude, Phanpy (Crystal), Nincada, Drilbur, Diglett, Onix and Wooper
Bug as we've seen a web perhaps hinting at a spider Pokemon. I would guess the spider is the main party member so it would be something akin to Ariados which is available at level 22 around the level this gym would be at.
Grass fairly easy type to beat and still relevantly early game, again we have a lack of them and seeing a forest perhaps hint at lots of grass types usable for the gym.
Ghost has no reasoning other than it is really under represented and it is in a similar place order to Morty and Fantina.
Water we have lots of good strong water types that could be used and we always get a Water gym (minus BW1). They've been 2nd, 4th and 8th the only even number left is 6 and it seems a good place considering how strong the next two types are.
Psychic we've seen what appears to be a Psychic gym and Psychic has always been a later game type in terms of gym leader/E4 because we've had 3 E4 members (Will, Lucian and Caitlin) and 2 Leaders (The twins (7th) and Sabrina (6th)). I've placed it in a similar position to the previous gyms.
Steel is a really resistant type with almost everything hitting it for not very effective it could be a great type and a lot of Steel types are late game; Aggron, Steelix, Metagross, Magnezone, Bisharp and Ferrothorn to name a few. We've seen the previous 2 Steel gyms as the 6th but neither have been challenging as they've had unevolved Pokemon on their rosters here hopefully their team will be fully evolved.
As for the E4
Electric we see it every gen, it could make for an interesting E4 team and it has some existing hard hitters that could be used in a late game team; Magnezone, Electivire, Eelektross, etc.
Dark has never been a gym and I don't think it will change this time. It seems to be a Game Freak favourite for E4 as it has been in every E4 minus Gen 4 since the type was introduced.
Fire because we've seen the pillars of flame and they have some formidable Pokemon; Arcanine, Darmanitan, Chandelure, etc.
And finally Fighting one of the most effective types in the game and has a lot of good Pokemon in Machoke, Mienshao, Conkeldurr, Lucario and Heracross say hello.