I'm in my 10th position over 30 years. I have only ever had one interview before being offered the job (two telephone interviews for jobs a long way from where I was living at the time and one mum offered me the job after the two hour phone interview and I had to say that I was sorry but I'd like to meet you first!)
I usually start with babies (two jobs the mums were still pregnant, this was 23 years ago when there was only 3 months maternity pay so I had one from 11 weeks old. The other from 4 months old) so I go when baby/babies (3 sets of twins, 4 months, 7 months and teeny tiny 11 week olds.) are napping and chat to the parents for an hour and then get to moon over/play with the baby while answering more questions/telling them what I expect from a job (to be paid on time, to finish work on time or to be told as soon as they are due to leave work (or train gets stuck) and to be updated regularly, do not phone me at 6:30 when I am supposed to be finishing work, that you are stuck in the office and don't know what time you'll be home and then rock up at 9pm without any other communication (and if you don't let me know, get home at 9 or later and then say, 'sorry, it was such a nice evening we decided to go for a drink on the river' you will no longer have a nanny!) and to show a little appreciation, thank you goes a long way, flowers a little further and a bottle of pink möet will get you a lot of lea way!!)
I usually get offered the job at the end of the interview (subject to references and as I am still in touch and see most of my ex-charges (godmother to two of their daughters) they are pretty good!)
I do tend to do quite a long hand over with mum, as the babies are usually quite little. Current charge was 5 months old when I started and I did a 3 week hand over with a week skiing in the middle. First set of twins were 5 weeks corrected and I did two months hand over as mum was very nervous leaving them, twin one was still in newborn clothes. Now both strapping 19 year olds and seeing twin 2 tomorrow!
Good luck, I realise this is such a daunting time for you and you can take as long as you need to find the right person for you and your family but I think when you know, you know!