I'll be honest. I have a huge bias in the distro choice, and preach Slackware to all. :cheesy: But I will be as far and honest in the matter as I can.
Slackware. It has BSD style init scripts which are very straight forward when cusomizing system initialization at all different runlevels. It can provide a low resource friendly environment, or provide a powerhouse of an OS. I have used it on machines as low as 120mhz/16k cache w/32mb ram and 1gb hd (even running X with blackbox if needed) all the way up to 2ghz 512mb RAM and hundreds of GB storage. Besides obviously the lack of GUI with low resources, the core still performs quick on slow systems. The kernel comes AFAIK totally vanilla, so you don't have to worry about any custom patches interfering with something you want to add on later. The sources can all be downloaded to everything that was built for the distro including the compile options used from slackware. This enables you to build the same software as slackware ships it, while also adding your own compile time option. Very handy! Releases come about twice a year. I would say that the biggest downfall is the lack of corporate support. Lots of commercial software written for Redhat can possibly run on slackware (VMWare for example) with some minor modifications, but not much seems to work "out-of-the-box." For some, this is no big deal, but when you have dead lines and compliancey issues, blah blah, you get the idea.... then this isn't gonna work.
Redhat 9 is not a terrible distro but I have had way too many pains with dependencies and what not using the package system, and it seems that any time i build something from source it doesn't work as well as I know that it should. Also, Redhat 9's support life is almost expired. Many say that Redhat is great for newbies, when really it isn't too much different than any of the other mainstream distros. From what I remember, Redhat 9 didn't even come with an mp3 decoder, yet came with a plethora of multimedia applications and as I recall the SQL that shipped with it was broken somehow.
Fedora is something that I have not messed with much, but if you are interested in Redhat, then you might as well just move over to Fedora.
Knoppix would be great for testing out your hardware to see what you can get working in linux before you actually install it.
I would boot up Knoppix to see what hardware is supported, and then I would install slackware! I would recommend doing a full install. (Around 2gb) If it turns out to not be right for you, then just try something else.