Current security reports indicate that while MS has improved their 0-day security flaw fixing, they are still behind both Mozilla and Google.
Sensitive data should never be handled on Internet Explorer and Safari. Firefox and Chrome are your best bets. I personally use Firefox, upgraded from FF4 to FF5 as it was released today, and it's a very solid browser, and absolutely the most flexible browser currently available. It can even be further locked down with NoScript, FlashBlock and a few other addons and tweaks. Also, you should consider using adequate security software solutions with integrated sandboxing features or using external sandbox apps.
Browsers crashing is not tolerable, as it's indeed an indication of high bug number and/or poorly maintained system. In your particular case, it does feel like the culprit is indeed IE9, which I would recommend against, even before knowing of your issues.
Regarding power options, it's something that DJs usually have to take a very careful approach, as it has a very significant impact on latency, an essential feature for live acts and such. But this isn't relevant for your situation, I think.
Overall, IE9 is less secure and lower performing than the top browsers, Firefox and Chrome, but not unsecure like Safari. There is also a third contender, a browser named Opera, and some people do prefer it over the top browsers. Still, there aren't enough pros for me to recommend IE9 for any scenario. I personally recommend Firefox, Chrome is too intrusive regarding user patterns and personal data. If you're that much in doubt install those three and see which feels right, as some people just work better with specific browsers.