Looking for 2-3 rooms flat in HD

I have recently arrived to Heidelberg because of the job I got here. I am going to stay here for a long term together with my family - wife and kids. I am now looking for not expensive family apartment.
Ideally flat should correspond to such criterion:
- Preferably located near the central part of the city: main railway station, Berheim , Weststadt, Kirchheim (but only north part of it) etc. Boxberg and the likes are considered as a last one if could not find anything in a meaningful time
- Flat should not be completely furnished except of the kitchen, kitchen should have furniture
- It should be 2-3 rooms with preferable area of 65-80 m²
Should have a bath :)
- I would accept price in a range 800-950 with utilities expenses included
- Flat should be available for a long term

Thanks