The first thing you need to know about owning ski boots is that it will be completely different than renting. A rental boot - even a new one will fit like a slipper as opposed to a performance sport shoe. This is partially due to the fitting process of rental boots which is designed to get you on the hill as fast as possible and not so much concerned with a custom fit, and partially because of the fact that the boot has been worn by so many differnet feet that it has broken down in ways that will never allow it to fit your foot well. Your own boots should be custom fit and I sugest you splurge on a custom footbed as well. A properly fit boot will fit you like a glove - snug but not tight.
With this in mind, is the Lange boot a good one for you? The key here is how it fits you. Each boot company tends to fit a typcial foot shape - Lange boots used to fit long narrow feet but I have to be honest with you I haven't had experience with Lange boots for a while so I don't know if that is still the case - I will talk to our hard goods buyer and see if I can fill you in on more details.
You also asked what the difference is between a beginner and advance boot and could you handle an advanced boot. Sometimes what a company refers as an 'advanced' boot is simply a more expensive boot with more features - a more advanced skiier is more likely to know how/why to use the added features and care about the performance options it allows them. Other boots are truly designed for advanced performance meaning they hold up to the rigors of high speed, advanced terrain and extreme conditions. This can spell trouble for a beginner because the advanced boots are often just too stiff for a beginner to flex. This will cause your performance to suffer as you will not be able to effectively execute your turns because you won't be able to drive your knee forward in the boot to get the ski to react.
So I would open up your purchase options, consider what features you want and look for a boot that will suit your foot shape the best with the features you want. To help you understand features check out
Skiing Tips: The Anatomy of a Ski Boot - Associated Content, and check out
Untitled Document I should be posting an article in the next few days about boot fitting that may help you out.
Take your time to make your decision. In my opinion it is the most important piece of equipment. Good luck with your search!