Before you decide on the Bike- or type of bike- Find an LBS (Local bike shop) that is going to suit you. It may not be the largest shop around but it will be one that offers advice- and can give you the info on the type of bike to get for your type of riding.
If it is just trail riding on smooth trails and nothing too aggressive- Then Cyclocross bikes may be the answer. If mainly tarmac then road or (Shudder here before you read it) A hybrid. Don't knock the hybrids. The good ones are a road bike with straight bars. OK not a true road bike but on smooth trails a lot more manoeverable and comfortable.
Now if you are talking full offroad up 15% hills on mud and gnarly rooted sections of Downhill- then a mountain bike is the way to go. Personally- I would not get a Full suspension within your budget. They may be full suspension but unless you double your budget- you could be buying a Pogo Stick.
A top rate Hardtail though is a different matter. The frame will be proven- the Front forks will work- instead of a budget pair that are Pogo sticks- and the components will be of a standard that will not let you down. Couple of manufacturers come to mind and top of my list for a proven quality bike is Kona. They make good bikes and all you have to do is decide the price and get the right size- You will have a good bike that is well sorted. Ask any Kona owner what bike to get and they will confirm my suggestion.
Just to show I am not biased- I Have a Giant road bike-A Bianchi MTB and a Cannondale Tandem. I also have a 12 year old Kona Explosif that is still the best bike I have ever had- but it is just like me and a little past it now, so has turned into the beater bike.
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How long was I in the army? Five foot seven.
Spike Milligan