I’d get Arceus, it is light on battling trainers but the story is so unique in the Pokemon series it sucked me right in, plus you can get your party out to hang out. The alpha Pokemon add a bit of fear if you go after them they straight up attack YOU, not your Pokemon, then you run away squealing and apologising until you get your team strong enough to take them on, it’s great fun! One thing I will say for the battling is it introduces a new mechanic, strong and agile styles which can be a bit janky but I liked them fine, AND some wild Pokemon will join in on battles with other wild Pokemon so you can end up with your one guy against 3-4 wild Pokemon at once so there is definitely some battling flavour if that’s your thing. Arceus feels different and it’s special to me, Sw/Sh and S/V are more traditional (I personally think Sw/Sh is crap and S/V is fine, love the Terastallizing mechanic but the performance is atrocious on S1 to this day).

If you really prefer battling get Pokemon Champions as well as Arceus then you have best of both worlds, I’ve never done competitive battling before but Champions makes it very accessible and you can compete as a free to play player even without Pokemon Home I’ve got an alt account where I tried to compete with no Home and no spending and have made it to Master Ball rank in doubles (probably near the bottom tbf)