I don't get a sense of what you are really looking for as the houses all vary hugely in price and size.
I'd think about how you want to live day to day, now and in the future.
Do you want a smaller mortgage and more disposable income, to have holidays with your DC?
Do you want a safe garden for her to play in and for you to entertain friends? Do you want a third bedroom as a WFH office space, or would it ideally be bigger so you can have friends to stay over and another child at some stage?
Do you want off street parking so you are not schlepping shopping and tired children along the street at the end of a busy day?
Do you love decorating and remodelling? Will your child thank you for spending every spare moment and bit of cash on updating a messy old house? Would it be better for you both to have somewhere you can move into and just start living?
Personally, I'd avoid any that need a lot of renovation. It's very expensive these days, such a hassle to find good tradesmen who aren't booked months in advance and so much disruption to daily life, not to mention unhealthy for children to be around plaster dust and solvents etc.
With all that in mind, so long as you can comfortably afford it, I'd go for the white house. It's pretty and spacious. There's room to grow and have another child or work from home or have friends to stay, private parking, a lovely garden, a cellar for suitcases and Christmas decs and all that clutter which gets in the way in smaller houses.