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Alpha Sapphire with the dexnav or what it's called is a lot of fun. I've never tried catching every mon before, but your progression being directly visible on the bottom screen is very motivating.
My entire team got Pokerus (another first for me) but I don't know who had it first. I'm suspecting the Poochyena with Thunder Fang from the first "sneak mission" thing the game encourages you to do. Lombre is the strongest member so far (though I haven't played much since Treecko evolved).
The nicknames have no deeper meanings. "Schnecko" can be translated to "Sluggo" or "Snailo", don't ask why that's his name, though.