I'm Episcopalian, so this is just one bird's (worm's?) eye view.
At least in the upper midwest, in the 21st century, memorial services (where the casket/body is not present) are much more common than actual funerals. Then the burial is a private, family affair (or the body is cremated.) Viewing, if offered, is usually at the funeral home. Open-casket funerals are not common (although this may be different in the south.)
Get your hands on a Book of Common Prayer. It has the funeral service in it, and it doesn't vary much. The service is fairly short, because often communion is also celebrated at a funeral.
Episcopalians often refer to themselves as "God's frozen choosen" (as do several other denominations) so there would probably not be any widow or mother throwing herself at the coffin, screaming and wailing. People pride themselves on their self-control, and crying at a funeral, even by the widow, is seen as "breaking down."
Emotional eulogies are usually not included. The only speaker may well be the priest, especially if he knew the deceased well. (Episcopalians call their ministers priests. They may be addressed as Rev. Sue, especially if they are female, but they are not called ministers or reverands by church members. Male priests -- who are usually married -- are almost univerally called "father" as in "Father David.")There would probably be lots and lots of flowers -- the acceptable way to show emotion. Amazing Grace is a very common funeral hymn. Yes, the congregation sings together, as at any other church service.
Everyone would likely be invited to the deceased's home afterwards, where light refreshments (finger sandwiches), tea and highballs (scotch, bourbon -- not margaritas) would be served. Sympathy & quiet stories of the deceased, some mildly humorous, would be shared. There would be no full funeral luncheon or wake.
Obviously, these are all stereotypes and your novel may well contain the exception.
If you have specific questions, feel free to PM me.
