I don't recommend getting any bike with breaks
. Brakes on the other hand......
Now that we've got that out of the way, what type of riding do you think you'll be doing? For cross country stuff, such as Lysterfield, Yarra Trails, Red Hill, the majority of You Yangs and Mt Buller, four or five inches (100-120mm) of suspension at each end is plenty. You certainly don't want any more if you're hoping to ride up hills with relative ease. Mega-travel (up to about 9 inches now!) downhill bikes are absolute dogs of things to ride on anything other than downhill tracks - the whole setup is optimised for going down as fast as possible with no concern about getting back to the top (they chuck 'em on the back of a truck for that!). As such, even competition-level bikes are heavier than your current ride! They need to be in order to withstand the impacts of big drops.
So, looking into the link that GreenAlias supplied, Giant is a really good starting point - bang-for-buck they're pretty much unbeatable, and the rear suspension system is one of the best on the market in terms of pedalling efficiency. For cross country/trail riding, look into the Anthem (4") or Trance (5") series.
The Anthem is targetted as a race bike, but you do NOT have to be a racer to get a huge amount of fun & experience out of it. The frame geometry is long & low, with a relatively short wheelbase (distance between front & rear axles) and steep angles, all aimed at speed & responsiveness, which can become a bit of a handful when the going gets lumpier. That said, it will still handle moderately rocky stuff surprisingly well with some firm guidance.
At 5" travel, the Trance is more of an all-rounder. Not only will the increased suspension handle bigger bumps, the frame setup us also a bit "softer" than the Anthem - it's a little bit shorter in the actual frame, so you sit up & back a little bit more, and the head & seat tube angles are laid back a bit more, which (especially at the front) takes a bit of twitchiness out of the steering, so it's more stable through lumpy stuff. As a result, it's also a more forgiving bike for the less experienced rider, not that the Anthem is particularly nasty.
Budget wise, don't look much below $2000 RRP.
Then there is the 26" vs 29" wheel debate. Many bike manufacturers now have decided that everyone wants to ride 29ers, and are making 26ers hard (or even impossible) to get, which is just a tad annoying. There is also 27.5"/650B in the mix, but these are not yet all that common. All wheelsizes have their pros & cons. The traditional 26" wheel is more responsive to steering, is a little bit stiffer, which also aids steering responsiveness, but tends to not roll as well as a bigger wheel, especially when the going gets rough. 29ers bludgeon their way over obstacles better than smaller wheels, but the bigger wheels do not get into corners as well, and require more effort from the rider to monster around a tight twisty course. Being an intermediate size, 27.5", at least on paper (I haven't had the chance to ride one yet, so can't offer real world feedback yet) should offer a compromise between the other two - better rolling than a 26er, and better handling than a 29er.
NOTE: I work in a shop that sells Giants. I ride an Anthem. It's a 26er because I'm not completely convinced by the marketing people that 29er is the ultimate solution they would like us to think it is.