Do a search with yahoo: "shop amd united states processor in a box" for listings and prices. Sorry I can't post the link. Of those 2, the 240 is newer but be sure to check the "cpu support" section of your motherboard manufacturer's website to see if your board needs a bios update to run the 240. If it's not listed, then it often won't post.
Here's a basic order:
Athlon II and phenom II are the newest with the Athlons being designed for lower end.
Athlon 64 is older (that's your 5600+)
Athlon XP is even older

The architecture of the new Athlon II is the same as the phenom II but without L3 cache. The advantage of an athlon II at 2.6 GHz (for example) is a lot compared to the older processors at the same speed. The new Athlon IIs even outperform the older phenoms at the same speed.