As Bednobs indicates, the term 'next of kin' has (with very few exceptions) little meaning in law. For most purposes you can nominate anyone you like as your next of kin. (It doesn't have to be a family member. It doesn't even have to be anyone you know. You can nominate Gordon Brown or Kylie Minogue as your next of kin if you like!).
Bednobs cites one of the few examples of a situation where the law does recognise a more formal definition of 'next of kin'. Additionally, if you were to die without leaving a will (i.e. intestate), the law defines a 'pecking order' of family members who can apply for 'letters of administration' (which empower them to distribute your estate in accordance with the intestacy rules). Assuming that you were to leave no spouse, your children would jointly top the 'pecking order'. (i.e. if the son you refer to is not your only child, but simply your oldest, he would not be higher up the list than his siblings. However, he would be higher than your mother).
Once again assuming that you died intestate (and left no spouse), your children would share your estate. (If you have just the one child, he would get everything; your mother would get nothing).
As Bednobs indicates, nobody is ever obliged to arrange a funeral. It would be up to your family members (and/or your friends) to choose who should make the arrangements. (Whoever was to make the arrangements could call upon your estate to pay for the funeral). If nobody agreed to arrange the funeral, your local council would be obliged to arrange a funeral. (They could reclaim the cost from your estate. However, if you left no money the council would have to foot the bill).
Chris