I currently work in a primary school office - following quite a drastic career change - and anyone who thinks it is a 'nice, easy little job' (as has often been said to me) would be in for a shock! This is all from an average sized Primary School point of view as I know things are a lot different in Secondary Schools due to the size of them. (Just so you know, there are 2 of us in our office and we do everything between us). I had never had experience when I got the job but I must have made a good impression as I got the job over others who were already working in other schools although I had worked as a volunteer in my childrens school.
Word processing skills and ideally SIMS experience would be the two things that would be most advantageous but SIMS is all in-house, so you can't just learn it unless you are employed. It is pretty simple once you have been using it a while though but it has huge functionality; not just looking up contact details but also recording attendance, generating reports etc.
There is also the finance side - again with the majority done using the in-house system. There is school funds, budgets, petty cash, trip money, dinner money, charity money.....having worked in a job with money handling would also work in your favour.
You have to be absolutely meticulous in record keeping as everything is audited and needs to be accounted for. For example, if you pay out £1.20 on stamps, you need that receipt as you can bet your life the auditors will pick up on it. You need to be really organised and be able to pick up where you left off - you could be in the middle of inputting something and the phone will ring, or a child will come in ill, or an irate parent will turn up and you have to break off from what you are doing to deal with it. Many people - and I think this is one of the reasons why schools don't take the chance on employing people who haven't worked in the same environment before - can't cope with the constant interruptions. A primary school I know employed someone as a business manager who, on paper, was great - he had worked for the LEA in a finance role - but once he was in school he just couldn't hack it.
You also have to be on your guard a lot and be careful what you say even if you think there are no children around. You can never, ever swear, you have to be careful when talking about Christmas etc. And it goes without saying that confidentiality is massively important. You need to be tactful, discreet, comforting, caring, sympathetic and often be able to bite your lip.
Above all, I think, you need to like being around children and be able to talk to them and show interest. Children tell you everything - from the mundane to the worrying and you need to be able to relate to them. Not being phased by vomit - or other bodily functions! - is another good one as believe me, you see and smell it all.
I love my job. It is so varied as you never know what the day will bring. You deal with lovely parents, horrible parents, social workers, education welfare officers, school nurses, other government bodies, governors, other schools, the general public....amongst others. You'll see kids who have a fantastic life, kids who have nothing, kids who are bullies and some who you just want to take home and give some love.
Hope that helps a bit - if you get an interview, be enthusiastic but realistic about what the job entails. Don't say you want it just for the holidays!