The built in routes for TC3 need quite a powerful machine. Cheapest upgrade, buy TRS2009 and look at other routes. I suspect you will still have some performance problems.
Your Celeron processor is lacking cache and then it gets interesting to look at the options. The cheapest is to replace your processor with an Intel P4, however they are getting a little rare these days and I think your video card is a little dated.
If you are not skilled in computers then I'd normally suggest a Dell but looking at their Australian site nothing seems to quite fit. The bigger the monitor resolution the more cpu you need to drive it. 1440 by 900 isn't bad resolution with something like a 2 or 5 ms second response.
Think in terms of $1100 to $1700 for a reasonable PC to run Trainz. Dual core would be nice, ideally the newer 45 nm items, they run cooler, 3/4 gigs of memory, separate video card see tomshardware.com for comparison but PCI 2 something like an nVidia GTX 260. Have a look at
www.newegg.com and look at the reviews, in general products with lots of reviews that are favourable are the sort of products you want to buy.
Compared to the cost of a model railway this isn't that bad. Many people who have an interest actually go for higher end machines.
www.computeronline.com.au has a section of customised PCs. Or look through the Dell machines, talk to them and see if they will sell you a 1440 by 900 monitor with a machine. You may need to go quad core with Dell to get a decent video card.
Probably some one with better local knowledge could guide you better.
Cheerio John