Before I start, I should point out that I'm a complete Linux newbie. I've only ever used it once, and that was a resounding failure. I was using Mandrake 9.1, and the rather poor computer I was using to run it wasn't really powerful enough to handle the graphical interfaces. Additionally, things were rather confusing (I'm a life-long Windows user).
I'd like to have another go at it. I've got a computer here with a 4Gb HDD, 64Mb RAM, GeForce2 MX and an AMD K6-2 300MHz processor that I'm wanting to run Linux on, but I need to know a few things first.

I'm planning on upgrading the computer to an AMD K6-2 500MHz processor shortly, but I don't know if I'll be able to get the component or not yet. As such...

1) What distribution (is that the right term?) of Linux would you recommend? I'll mainly be using the computer to run an IRC bot of some form, and possibly to download files.

2) Will the above-recommended distribution (?) run well on the computer specified above (the 300MHz one, or if not, 500MHz)?

3) Bear in mind that I'm a complete newbie here, but can I get both a plain command prompt and also a Windows-like GUI on the recommended distribution? ie: a command prompt just on its own without having to load a GUI?

4) Is it possible to get a BitTorrent client that works on Linux, and if so, does it require a GUI or will it run from a command prompt?

5) Would it be possible to network the computer once it is running Linux to a computer running Windows XP Home SP1 through a Linksys BEFSR41 router (I believe the router will act as a network hub)?

[Edit: Added question 5]

1) you got the term right. lots of people also call them 'flavors'. fedora.redhat.com, suse (from novell), mandrake would all probably be good fits for you. http://iso.linuxquestions.org/

2) sure, why not. i know someone running gnome on a 200mhz with no complaints.

3) yes. (you can change the default runlevel -- graphical or not graphical are options -- by editing /etc/inittab)

4) yes and yes. lots of clients available.

5) yes. samba lets linux share files (i assume that's your goal)

Just to add:
1) You may want to try a slightly lighter distro like slackware or vector until you get your upgrade.

2) Distributions such as Fedora tend to be slightly more sluggish due to the number of bundled applications. The performance would be much better with a smaller distro. Don't forget you can download ISOs from:
http://www.lqiso.org

5) Certainly. Just configure the IP addresses or use dhcp if your router acts as a dhcp server.

Lots of help! Thanks a lot .