Spend a day at one of the big camping places where loads of tents are set up.
GoOutdoors, or SK Camping in Surrey if nearby or similar.
Go inside all the tents and imagine your family in them.
Do you want a big porch - can this be an extension?
Do you want to be able to put it up by yourself (simple tunnel or pop up construction) .
How heavy / bulky can the bag be? Will you ever go to the beautiful wild / woodland sites where you take your stuff to the pitch b barrow? Steel poles add a lot of weight and bulk over fibreglass.
Is there a little shelter over the roof or a door not on a big slope - i.e will water pour in when you unzip in rain?
Do you want blue or green, a.n other colour, or don't you care?
YES you need a minimum of 3000 HH - 3000 is fine for the UK if a good quality tent - the devil is in the seams - look for taped.
Groundsheet - yes sewn in - a footprint under your tent is relatively inexpensive and saves your whole tent being on a muddy / wet ground for a wet pack up.
In your place, for 4 night stays, I would look at the Vango Icarus or similar: roomy, easy to put up, the Vango tension band system makes it good in wind.
I have not had a close encounter with an inflatable tent - I wonder how long they take to pack up - getting all the air out to fold? They are also heavier.