My first flat can only be described as a shit hole. It took months to transform it, lack of money, lack of time and lack of interest as it wasn't exactly a priority, I spent months without furniture and slept on the floor for at least 2 months until I could afford a bed. So I am pretty familiar with compromises.
Nowadays, my non negotiable requirements:
detached
commutable to central London
excellent schools
parking, at least a private drive for 2 cars
quiet road (but would have considered leaving near a school as the school run doesn't really clash with our working hours)
nowhere near any flood risk
obviously the number of rooms I need as a minimum.
Then it's more about the general aspect of the house, I need space, but would have compromised with open plan downstairs (which I hate) if needed, with number of rooms depending on their sizes.
It's interesting that a south-facing garden is so important for so many people, worth remembering when you intend to sell soon. I have never given it any thoughts, there's always sun in the garden at some point during the day anyway.
Downstairs loo, utilities etc.. are nice, but you can always add them later, so it's not a big deal for me.