You are right, if you stuck with zeus and the included PSU they you would probably fine running an Athon II X3 and integrated graphics.
However, if you ever wanted to add a decent graphics card you would need to buy a new PSU.
One thing I would suggest is that you could drop the RAM ammount down to 2GB. For desktop uses this will be more than sufficient and this money can be used to buy the quality case and PSU - which will stand you in good stead for the future.
New hardware from both Intel and AMD is coming out early next year. From reports it will be a fair chunk faster than existing tech, however how it will affect the low-end components is unclear. If you need a system now - then there is no point waiting, however if you won't get all the money together until then it may be worth waiting or buying the non-core components (Case, PSU) sooner and hold off on the mobo, CPU and RAM until the new releases.
As for unlocking, the AMD Athlon II X3 is actually an X4 (quad core) with one core locked off. Often this is because one of the cores is damaged - so AMD can still sell a borked-up quad core as a fully functional triple core. However, often they will just disable a core on a functional quad core and sell it as a triple core (usually isn't enough broken ones) - in these cases the user can unlock the fourth core themselves and get a functional quad core, while only paying for a triple. To do this you need an AMD 7 series motherboard with a 710 or 750 southbridge. The 8 series also do unlocking and these have really taken it to heart as it is usually offered as an option advertised by the board manufacturer. So to restate: unlocking the fourth core is not a certainty and you will require a motherboard with the correct southbridge, however if you do get lucky then it is certainly a nice thing to have.
As for overclocking, you just need to raise the Hypertransport bus speed with these athlon II chips - how well you can do this depends on the motherboard, the chip and the amount of voltage you are prepared to give it. However, I know very little about AMD overclocking, so you would be best to ask other about this (specifically BigWayne).