unfortunatly here in britain everything costs a bloody fortune so little fourteen year old boy can;t afford an ethernet card or nething frivilous like that for a home network so i can't offer any help there. however, you might want to try http://www.linuxdoc.com
and look at the hardware-howto which shows supported hardware in linux (not completely comprehensive but close). that should helpl you get one that will work (and might point you in the direction for advice in getting it to work)
red hat 7.1 did have some probs (bugs etc). the earlier versions are better (make sure you have all the patches).
as for the mouse i have no idea, generic drivers tend to work for pretty much all mice. try updating xfree (i think that it's at 4.0.3 or something like that).