What would I look for on my computer to find out which distro is optimized for it?

the only thing i can think of in terms of "optimized" for particular machine is compiler optimization. That is when you set the compiler to use and take advantage of the features of your particular cpu as opposed to just producing old old style code made to run on cpus from 1983.
so basically you need a distribution that is compiled by you like gentoo where you take controll of the compiler flags and optimization level.

there is often alot of cross talk on this point where peple say compiler optimization doesn't help and is a myth etc etc....
people that talk like this are wrong however and compiler optimization can make a huge difference.

here is a test example from my machine.
with "gcc -march=athlon-xp -O3 -ffast-math" as the compiler setting
I get an overall tested speed increase of 13% over generic "gcc -O2"
almabech (astronomical calculations) runs 35% faster !
when you combine these speed increases over various software layers
the performance increase can be quite dramatic.

I think optimization comes with understanding.
The deeper you understand what you need or don't need to run linux, the better.
Then you can also build your own kernel
Or you can compile a distro like gentoo on it
Last but not least you can try to build LFS (Linux from scratch).

There are two ways to approach this.

1. What role is your computer playing - server, scientific workstation, desktop?

2. What type CPU does your computer have - i386, PPC, Sparc?

You can browse distros at http://distrowatch.com/

and then check the requirements for any distro on that distro's homepage.

If you have a laptop or desktop made in the last three years any popular distro can be a good candidate for optimization. Of course, if you don't have special needs you may find optimization isn't needed.

Dennisk