Vacuum Cleaners Discussions

I just found this site. I really need to get a new vacuum cleaner. Right now I just have a Eureka Mighty Mite with a HEPA filter. I have recently taken in a long-haired chihuahua and a cat (for a friend who is not able to care for them any longer). I am allergic to (and have also grown very fond of) both the cat and dog and I also have quite bad dust, mold, and pollen allergies. I live in an older split level house: the two upper floors are bare wood with no rugs and the lower two floors are covered with wall-to-wall very-low-pile commercial carpet. The cat (bless her) is generally content to voluntarily stay in the basement all of the time with the exception of just one or two very brief morning strolls each day to the next two higher floors. She sheds what seems to a cat neophyte like myself to be an enormous amount of fur but I'm told by friends who are cat owners that it is a normal amount. The chihuahua just wants to be in the same room with me although I have kept her out of the bedrooms and bathroom on the top floor. I have looked at quite a few vacuum cleaners from the very inexpensive to Miele and Lindhaus and I still am unsure of what to get. I've never had to deal with pet hair and dander before. What would work best for pet hair and dander on low-pile commercial carpet and still be good for bare wood floors and have a good filtering system for allergens? I do know that I would like the self sealing type of bag that is in the Miele (and perhaps other brands?) because of my allergy problems. I can spend up to $850 if I have to but it would be much better for my budget to spend less. I'm sorry for the long-winded description. Advice would be very much appreciated. Thank you.