Right so this isn't your first run around car at 17/18 so you needs are different. In your case I would be looking at those insurance groups on AutoTrader. I have to say AutoTrader is a brilliant tool for narrowing down by price, by year etc.
You want safe as safe can be because you have children in the car with you and big enough that you can get your children in easily. You need to look for less obvious cars like Kia, Hyundai (same factory pretty much) Toyota and Skoda (it's a VW/Seat underneath) lots of car manufacturers are the same company.
Autotrader will allow you to narrow down by size too, city car, small SUV etc. You are using it as a tool to find cars and then run the plates for actual quotes. CompareTheMarket holds all the details you just keep changing the make and model of the car and the plate, keep running the numbers. Also have a look at https://www.euroncap.com/en to see how safe your car is.
Buying I would go through a dealer but please pay £200 for AA or similar to do an independent mechanical/body check on the car. This is your golden ticket if anything goes wrong with the car. I bought a 2 year old car and had to return it due to a fault they couldn't fix. The fact that the AA also noted the same fault meant I had strong evidence rather than just my word saying there was an issue on the test drive.
Best car I had, Hyundai iX20 (a sportier model than the i20 same as Kia Venga) reliable, never in the garage, had it almost a decade. Brilliant car.