Sounds like you pretty much know what you need. Be aware that more gears doesn't necessarily mean a wider range - 21 speed bikes can have just as wide a range as 30 speed bikes. But more gears does mean more choices, more likelihood that you'll find a comfortable gear under a wider variety of riding conditions. Upright position and hills means that either a hybrid or a Mt. bike can suit your needs. Unfortunately, neither is particularly light.
Brand is not particularly important these days. All the big companies (Giant, Scwhinn, Canondale, Specialized, Trek, etc.) make decent entry-level Mt. and Hybrid bikes in your price range. All will be similarly equipped.
But, since weight is an issue for you, you might also consider a lightweight road bike with a high stem and ask the shop to equip if with classic English 3-speed handlebars and brake levers and rapid fire or twist shifters to handle the wide range gearing you'll want. Another handlebar option for you might be the less common but highly versatile "Butterfly" or "Trekking" bars. (sold at "harriscyclery.com" among other places). However, I don't know if you can get an decent road bike with these conversions for the price you want to pay.
Much more important than brand is the shop you buy it from. They should have a reputation for good service, and a staffer trained to properly fit the bike to you and willing to take the time to do it right. There is no bike worse than one than doesn't fit properly and no bike better than the one you like to ride.