I've just started my re-watch of season 1, and I do agree it's a bit weak as compared to later seasons, but as said, that's just because they're just starting off and figuring out what they want to be.
The arc of "let's find dad" - well, God Himself (aka Chuck, aka, Kripke) said that he specifically made it a fairly light arc in order to get us into the show easily. It's mostly standalones, some good some bad some average, but even then the trademark tie-the-monster-of-the-week-into-the-boys'-personal-issues was there right from the beginning.
I'm still in the Urban Legends phase of the show right now, before the arc proper has started to kick in. But like Babylon 5
, I'm finding that a lot of stuff was set up even this early that ends up being vital later on. In retrospect it's clear that Lucifer's plan was already in action as of the pre-credits sequence of the very first episode. With what we know by "Swan Song," it's possible to see the connections all the way back to "Woman in White."
And the little things - the first demon possession happens in "Phantom Traveller," episode 4. The first hints of Sam's supernatural abilities come in "Bloody Mary," episode 5. Both of those things obviously become much more apparent as the show prgresses, but I like that it's all right there from the start.
Oh, and yes, "In My Time of Dying" is one f'ing awesome season premier.