Hey guys so my girlfriend (155cm) is looking to start cycling and she plans on trying some of the bicycle trails in Melbourne, like the Capital City Trail.
Anyway, she is still a beginner and only feels comfortable on low bikes where she can easily stand on her feet when needed. She is willing to spend in the region of $300 for a good bicycle and is happy to purchase second hand. To complicate things further, her brother who is slightly taller than her would also like to occasionally ride the bicycle.
Of course the priority is that she is able to comfortably ride it and all suggestions are greatly appreciated!
If your GF is a beginner I would take her to a local bike shop and get her to try some, get her to find out what size and what type she likes. I'm not necessarily suggesting you buy one from them but at least let her get the feel.
You'll probably be looking at one of two bike types a mountain bike or a hybrid. A Hybrid is somewhere between a mountain bike and a road bike and are generally comfortable. Mountain bikes are general pretty comfortable but on roads/cycle paths take more effort to keep them going (mainly because of the wide tyre tread).
Gumtree always has a lot of second hand bikes up for sale, also try Bike exchange (http://www.bikeexchange.com.au/).
Cell Bikes are good for cheapish (but good) new bikes (www.cellbikes.com.au). (Don't by a fixie though for your GF even if it looks cheap, it's not what you want).