UT has a robust stats tracking system built in. That gametracker site just hooks into that I believe.
http://ut2004stats.epicgames.com/
I've actually recommended playing bots before and a number of experienced players have given me flak for it. The trick is to put them above your level, either slightly or way, play around with the game speed (usually make it faster, I either do 110% or 130%) and as you said, do weapon arena at first so you can focus on a single weapon. As soon as you beat a bot, go to the next skill level. The way I practiced was on a 1v1 map against a bot that could beat me. If you can get to the point of beating a godlike bot at 130% gamespeed, you will fuck up 80+% of the players out there. Don't confuse bots for people though. The best players are good because they're clever and have thousands of hours of experience that make them difficult to hit even when they're not looking at you.
Mud and I played around with training for hours. I saw marked improvements with both of us even though we're at different skill levels. If you get me talking about weapon strategies I won't shut up (as Mud will attest), but I know I saw him using rocket techniques I showed him to take out a guy 1v1 who thought he was better (who also consistently said 'wtf' when Mud killed him). The point there is that we trained specific things atomically, meaning training dodging, rockets (aiming, straffing, suiciding, charging *individually*), goo, shock, etc. My piano teacher used to say 'Practice doesn't make perfect, perfect practice makes perfect'. Playing is not practice.
I actually enjoyed the training we were doing more than normal games at one point. It becomes almost zen like and the hours kindof melt away (we had all weapons, infinite ammo and no score). I'd offer to help, but haven't been playing lately and those melting hours usually occured between 10pm and 6am...
Also, it's important to understand your strengths and weaknesses. Take your opponent out of their game and try to bring them into yours. For example many hitscanners are comparitively weak close range. They'll brag that they can hit you with shock from wherever... unless you're consistently doing 180 degree dodge strafes while shooting rockets at their feet. Poke around at their model (get inside their head) and try to identify weak points, though at some point you will want to go against someones strength in order to build yourself up as well.
Anyways, these are just words. I claim no authority as a player.