Mine was solid all the way up to top speed - on a decent surface. Start with looking at rear pre-load and tyre pressures,then tyre condition and any loading of accessories.
Poor surfaces throwing it off is a different issue. A good budget suspension upgrade is to fit cartridge emulators to the front fork and a stiffer spring to the stock rear shock. After that you can replace the shock and at the front fitting a complete 636 fork set is a mod that several people have done.
Again, on your bike, given its age, you may have a rear shock that no longer does its job, and the same for your forks, so try to figure out what the problems are before you decide how to spend money on it. It's also worth checking that a previous owner hasn't dropped the yolks too far down the forks and screwed the steering geometry.
Without really knowing what you're unhappy about its hard to suggest more, but these are a budget bike and there's scope for improvement. I doubt if the bars will help handling much, but if they make you feel more comfortable that in itself is a help.
Personally, after checking everything is as it should be, I'd start suspension upgrades with the rear shock.
Rob
