In my church we have a memorial (without the casket) service as opposed to a funeral. Most of those attending a memorial at my church are not regular church goers, so there is no real appreciation for the finer pieces of literature written for the organ. As people are entering the church, they are greeting one another, greeting the family of the deceased, and generally chatting with other attendees - the music then becomes musak - something to fill the space.
With that in mind, I don't spend/waste the time preparing major pieces for my prelude ... the prattle coming from the pews is just too annoying, and it's something that we can't change. The "unchurched" have no idea of what to do when entering a holy worship space. To them it is just another public hall - a restaurant - a social gathering spot. Yes, that irks me to no end ... If I play louder, the "din" also becomes the same. But, the $$ is great, and that is how I make my living besides my government retirement pension.
I do, however, play a postlude at the conclusion ... usually A Mighty Fortress Is Our God from a collection of the same name which contains compositions by several famous composers: Reger, Buxtehude, Pachelbel, Pretorius.
There are the rare occasions when there is a specific request for music - we try to make that as part of the service, perhaps where the offertory would occur if it were a normal Sunday service. Same is true for vocal solos.