Hi OP, firstly I just want to say that it's not as complicated as some people may suggest - and done in the right way a 50/50 split can have very little impact on the child's lives.
I have 3 dsc (4, 5 and 8) and the set up is as follows:
Sunday 1pm - Sunday 1pm. One week at mums and one week at dads.
The dsc have everything they need at each home - school clothes, shoes, bags, normal clothes, jackets, pj's, everything. This ensures that there is no 'packing to leave' at the end of the week. Kids just go back wearing what they arrived in.
I would suggest, when the person moving out has sorted a new house etc that the main house divides up the kids things so that there is a 'float' so to speak which can be added to by the other parent.
My dp was the one who left with the 'float' so has added to it over the years and things just become part of the kids lives at dad's. Obviously if money is tight and it was for dp then things like ipads, computers, books etc went between each home until birthdays, Christmas etc when dp would get the kids things to keep at dad's.
Regarding money (in our situation) no money changes hands. We simply pay all fees etc for the weeks we have the kids and mum pays for her weeks - same with clubs and other expenses.
School trips are divided and each parent pays half.
In our situation, mum gets all tax credits and cb and that is fine. (That was part of the 50/50 agreement) but you would need to think about how you wish to work that.
School runs are done by whoever has the kids on that week. And the parent for that week takes them to all clubs etc.
On our weeks mum doesn't see the boys at all but on mums week DP arranges to see them midweek as he doesn't like to go a full week without contact.
Communication is key though, because sometimes things change and it's good to be flexible - managed correctly then the dc will not see any animosity between parents and in our case, boys mum and I have struck up a nice relationship, but I imagine that's a long way down the line for you.
Both parents attend all parents evening, school letters that come home are photographed and shared with the other parent on receipt.
DP ensures boys visit his family and mum ensures same for her family.
This situation really works for us. Best of both worlds really. Means you have every other weekend to socialise and do your own thing knowing that dc are happy with the other parent. On your weeks you get to do all the parent stuff - kids don't miss out on equal time with each parent and the other parent doesn't miss out on being a parent and all it entails.
Sorry about the massive post, but I am a real advocate of this scenario because for us, it works.
You are welcome to ask anything at all.