I run on a 2year old toshiba Satellite p205d, Its an AMD Turion X2 at 1.86ghz, the thing is all jacked up and slow from to much crap but it runs UO like a beauty!
I sometimes lag during pvp fests, but thats probobly due more to using free internet from someone in the neighborhood than the computer itself.
I bought my laptop for 900 2 years ago, its only worth about 350 now.
Craigslist is a good spot to start. Can get some laptops that if you just want to run UO you will only need to spend 200-300 bucks. And thats probobly overkill.
Also with Xmas coming and New Years, theres going to be ALL sorts of sales running on those days. Might hold out for that. I know I will be gettign a new Laptop or Desktop on one of those days (Xmas Eve, or New Years)