A question to ask yourself - how often do you expect, really, to fly with the family?
An enjoyable 2-seater on a permit, such as the Luscombe above - or many other possibilities - will for most of us give many hours of inexpensive and enjoyable solo or 2-up flying, then hire something like a C172 for the half dozen hours per year you'll find you actually want a 4-seater.
I would also however agree with those saying "go for a share". Owning around a sixth or eighth share will massively cut your risk and fixed outgoings, and if anything increase the availability compared to spending a lot of your free time looking after a sole-owned asset.
G
(Owned shares from half to twentieth in 7 aeroplanes, over about 20 years.)