You won't get good at UT without playing it for hours and hours and hours.
You'll first need to get used to the dynamics of using different types of weapons, hit scan weapons for example (Shock, Sniper) require much more accurate aim especially at distance and will make you sway towards lower mouse sensitivities and less movement, where as spam weapons like flak and rox are more for close combat and you'll want a higher sensitivity for these situations utilising more movement with a more random pattern to avoid spam from everyone else.
It's all about finding a balance point (personally I have a high sensitivity because over time I've gotten better at mouse control and so can aim with it at range, thus making it good for every situation). Initially you prolly won't be able to do this, start with a lower one so you can aim the hitscan weapons better (The hardest ones to get used to), but if you start getting frustrated with not being able to turn quick enough when someone is dodging round you, push your sensitivity up a bit and keep going like that
Map tactics are important too, most importantly time the important pickups.... shield belt and damage amp if they're turned on, along with decent ammo spawns (Ammo i find is much more important in UT3 than older UT games, it seems to run out a lot quicker).
That's barely scratching the surface and only touching on DM, there is A LOT to learn and get good at, to be good at just one game mode, let alone more than one.
I play for a team that managed to hit the top in UT2004 ONS and then was fast climbing the ladder in TDM with A LOT of hours clocked up, so can help you out if you need any advice.
) But I like the flak cannon and stinger assault gun too.
