Since it's only for your exam, better save the money for something else / better build.
I'd usually ask for the components details, but with the PSU and mobo gone, in this case, it doesn't matter. It won't hurt to post it anyway though.
No need to also change the CPU, just make sure the motherboard is compatible with the Celeron. Unless you want to upgrade the whole platform and decided to use it other than for your exam. But that kind of defeats the purpose of a practicing object (or practicing PC? which one is it?).
As for the RAM, if you find it cheap enough to be negligible, go for it. 512 of RAM isn't a enough for seamless computing, even for light tasking. Unless you have the patience to wait for lags and freezes. One thing though, since it's an old system, considering it only supports DDR1 (just hope not!), the price is usually more expensive than the DDR2.
Any cheap unbranded PSU will do just fine if budget is your concern. I assume the PC is not using any discrete GPU, thus making the power requirement low. I's estimate that a 300W PSU will do just fine.
Does this practicing involves installing / re-installing PC components besides testing equipments (whatever that "equipment" term means )? Because if it does, having another 512MB of RAM will be a good thing, since the more complex the setup, the harder the troubleshooting will be.
Ah, reminds me of my younger days (as if I'm already old)...