As clefty says, also if you wanted to build your own it is doable with that budget but a mix of second-hand parts and new would give you more choices. It would be more time and labour intensive than just buying one. However, you would also learn more about your bike than simply going out and buying one and in that sense it would be more rewarding. Ask yourself how much time you have to spend on such a project and do you have a local bike shop not too far from where you live that you could trust if you get stuck during the build and need help.
As clefty says, also if you wanted to build your own it is doable with that budget but a mix of second-hand parts and new would give you more choices. It would be more time and labour intensive than just buying one. However, you would also learn more about your bike than simply going out and buying one and in that sense it would be more rewarding. Ask yourself how much time you have to spend on such a project and do you have a local bike shop not too far from where you live that you could trust if you get stuck during the build and need help.