In terms of the money going to a band from album sales, does it matter when I buy the album? Is there a difference between day of release, one month later, one year, one decade? I would guess this is dependent on contracts signed and probably copyright law (lets assume US), but is there a commonality at all across labels and artists?
This Fusion.net article answers your question better than I ever could (and also probably in more words than a StackExchange post would allow), but I'll summarize it here.
It doesn't really matter when you buy an album, so much as where. As this article calculated, if a band with four members that writes their own songs sold 500,000 copies of an album at $16 apiece, with all of the random fees, deductions, and expenses, they could only wind up with under $12,000 per person. Now, this article takes over half of the price of the album for the distributor (22%) and the retailer (30%), so eliminating one or both of those could leave the artist with more of the profits. That's why, as the Fusion.net article pointed out, you should purchase the album on the artist's website or at one of their shows.
And as for shows, seeing them live is really the best way to support an artist (aside from just sending them a bunch of money, of course). Almost all artists, whether they're international superstars, regional hit-makers, or local bands just starting out, make the majority of their money from live performances and touring. And anything of the artist's that you purchase at the show, whether it be an album, a t-shirt, or a Snuggie, won't have as many hands taking cuts of the profits away from the artist. The same thing goes for purchasing them from the artist's website, though even then there's likely an ecommerce company, like Shopify or Spinshop, taking a cut.