Yeah lol he does call her "Ichiban", which roughly means first, or the best. So yeah he's calling Jun-chan better than his wife lol. Then he says that since the annoying person has left, he can finally meet her. And yeah the saifu basically means wallet, so in her case it's a purse.

That said though, I don't think you need to understand what they are saying it to get the humour. But understanding some of the things he says to Jun-chan in game is kind of hilarious, especially since he gets caught badmouthing his wife. I thought it was funny in a funny way, not funny in the crazy absurd japanese commercials that end up on youtube way. I remember one where a woman gives birth to a horse iirc. Yeah...I've seen some ridiculous Japanese adverts and am glad this isn't one of those.