Hey, Thanks for the props on the site, and welcome!
I work in Sales (Although House Sales), and i can honestly say that you are not the only one that buys unseen. It's not too risky so long as you trust the person who is selling it to you.
It sounds like the car would suit your needs in terms of reliability and economy, as well as shelf-life. I've seen '70s Corollas with 500,000km on the clock and still running like new, so its really a matter of looking after it.
As for the space, you should be able to fit a stroller and such in the boot, but if you are looking for real space, go for an older Camry. But thats just my opinion.
All in all, it should suit your needs, should last, and should be a good car. Good luck