Really depends on location and type of house I would have thought?
My universal must haves are a manageable garden with a good aspect. I think light is very important and often people don't realise that either their house is going to be baking on one side all summer and in cold darkness the other all winter. Where rooms are in relation to the sun really matters to me. Also walkable access to good public transport.
In a terrace I would look for side-access (but not a house on the corner) and decent fences, a loft extension or extendable loft. Good floors too. A kitchen/diner but not open plan and a sink that faces a window. A box room that is actually suitable as a small bedroom/office. A combie boiler and sound electrics. A downstairs loo would be a boon. As many original features as possible. Ideally structurally sound and a utility room would be fab, but unlikely in our price bracket.
In a detatched house, again, clearly defined dboundaries and a good aspect, nice flow throughout house and no clunky add-ons (dark dining rooms in the middle of the house because of extensions, ropey sunrooms, kitchen renos with a toilet in a cupboard etc).
My deal breakers would be end of a street or on a corner (too exposed/busy), too near shops, garage or main road, weird shared path and access arrangements. Primary schools are fine to be located near (traffic controls and quiet summers), but secondaries and colleges not so much. Also not keen on open plan.
We could never afford anything that had been "done up" as in new kitchen, back extension etc, but also don't want to be in a fixer upper.
Thinking about it though these all very specific to time of life. If you had asked me 20 years ago, nurseries and schools would have been top of the list. Currently "my must have" would be living somewhere where not everyone is redoing their entire house all the time (3 years into next door's neverending rennovations and now the other side are starting on their extension!) Argh.