I asked the same question a while ago. Lots of people recommended the vango icarus 500.
I eventually got a vango juno 500 as it was on offer at £32 and I've never been camping before so didn't want to spend a fortune before deciding that this is the life for me!! The juno is a tipi type tent so no living area - no good for what you're looking for. But I managed to get it up in 10 mins first time which is a huge bonus!
The tent I'm aiming for is the hypercamp eldorado which is a pyramid tent that I'm assured can be erected single-handedly. Works out at just under £200 delivered. There's a lovely thread of pics of the inside on ukcampsite forum. It was originally pale grey and blue in its first incarnation which I think looked lovely.
I have a Quechua 4man 2 seconds plus pop up tent. It's up in moments. It has a sleeping area and a porch big enough for sitting in in chairs. We put a windbreak up outside it for our cooking area. It's down in minutes too, but you should practice. Fab not having to wait long with a youngster.
There is a huge range! From the Quechua, through the Vangos to the belltents (DH can pitch our 4m diametere one alone and no way you'd need that with a small family).
Find a few you like then watch pitching videos on sites and youtube, should give a good idea. Watch out for too high roof lines (unless a single pole design) or very ehavy tents that need two to lift / locate.
I've just ordered a Vango Kairos 400 which apparently can be pitched in 5 mins. I have a bell tent but it is quite heavy to put up completely on your own as someone needs to hold the pole whilst you peg out a few guys to keep it upright.