The P3/256MB ram would be plenty for the task, but the other
concern is what the motherboard supports, your available
hard drives for example.  I have a very reliable Celeron 500
(or is it 533?  It's been so long I don't remember)
fileserver that just won't die, I put a gigabit ethernet
card in it a few years ago and it still just keeps on
ticking like a timex watch, sans the rare HDD failures we'd
expect every few years.

SiI0680 can do the job, though having a couple of those in
use I find them a little fickle.  They seem to like
degrading the ATA mode to lower than a typical mobo ata
controller would.  I mean their logs show and warn it is
happening.  This may be a control-freak scenario, if utmost
performance isn't needed, it would be no big deal if they
degrade to ATA66 or even ATA33, but it can cause some time
spent determining why and time googling for reasons when
people randomly suggest things like bad power or data cables
when an otherwise same system can run the drives ok on same
power and cables.

In other words, SiI0680 is a good budget choice to just get
raid, but performance may suffer.  For many people's
fileserver needs it may not matter, just be aware if it
throws you a curve in ATA mode warnings.

Any of the above systems have ample performance, more than
enough.  PCI bus with a raid card will bottleneck more than
cpu or memory amounts for a limited # of users with a home
fileserver.  Some chipsets are worse for PCI performance
than others, Via in particular was bad for it and I wouldn't
trust their current chipsets due to how many chipsets they
released over and over and over without any bother to
attempt correcting the problem.  So it's back to motherboard
since 256MB and the CPUs listed are plenty.

Then there's power.  The P3 system will automatically use
less power, and the core2 combo has  idle plus more voltage
and multiplier options to reduce power.  The central idea
here is that for a low concurrent user scenario, the P3
900MHz is even more than you need, if lowering power
consumption is important you might actually consider
underclocking that.  No kidding, it might make only a
trivial difference in performance but shave a few KWH off
your electric bill.

The idea is that if you use the older  parts, the newer ones
remain available for other purposes.  If you would have a
random scenario where the newer parts would be thrown away
otherwise, by alll means then use the Core2 system with more
memory - but it won't make much difference, the bottlenecks
in this use are primarily PCI bus and HDD individual
performance.

I must confess that I have played around with a lot of
various hardware towards the goal you have.  Basically you
need to decide which is most important. Power, performance,
or cost/resale of parts.  Then rank those as relative to
each other.  If performance is important (for limited user
home fileserver), it's not the memory or CPU that matter as
much as having a raid controller that isn't on the PCI bus,
and same for the ethernet.  However, there is much to be
said for doing things dirt cheap and still reliably, having
either or both on the PCI bus you can still have 30+MB/s if
a decent (Sis, nVidia or Intel) chipset and drives more than
a few years old... and of course gigabit ethernet.

i suppose I assumed gigabit ethernet, if you don't have that
then none of the above matters, there's nothing that can't
saturate 100Mb made in the past 8 years.

Although RAID 1 makes sense as protection from a single drive's catastrophic
failure...
it would be of no use in the event of file system corruption or contagion.

I do not think it a good practice to contain all your important data in one
central location.
The real key to data backup is to store it in as many different locations as
possible.

Rather than set up a central server...I'd add one large drive to each of
your machines
and keep your important data in *every* location. Your data would be
extremely safe with such a scheme...
and I'm sure there are plenty of synchronization methods available.