I am a licened funeral director and have delt with this issue many times. Unfortuantly this is the hardest part of the job. The suggestions that everyone has give are correct and helpfull.
The ss office will give a burial benifit but it is not given untill a month or so later, and is only a couple hundred dollars.
If you donate her body you will not recieve her ashes until a year or so later.
If you use the assitance program for low/ no income and turn her over for the county to give her a burial. The reality of this is that she will be cremated and her ashes will be dumped in the back of a cemetery with others, DO NOT GO this way.
If she or your father are in the military you can go this route, but you will still be paying around 5,000 for the service and burial.
My suggestion would be if you wish to go down the cremation route, find a funeral home that does their own onsite cremations and do a direct cremation, then goto your church if you belong to one or a local church and see if they will allow you to have a service. You should not be paying any more than 700 for the cremation, if you are they are ripping you off, find somewhere else. The church is not going to charge anything, and you can find a cheap book to use as a register book at walmart or target. Go to your local copy center and see if they will make you some basic service folders, these should be fairly cheap as well.
If you want to go the burial route, with no visitation, tell them that you don't want embalming and that you just want a graveside service. This will cost you anywhere from 3000 up depending on the casket.
Basic things to keep in mind:
You can order the same casket or urn that they have at the funeral home for a third of the cost if you order it online.
If you bring your own register book, and service folders you will saver anywhere from $150 upwards
Most funeral homes will charge an upcharge if you order the Obit and flowers through them, so order directly through the paper and the flower shops. Be careful some papers will only take obits through a funeral home so look into this.
Make sure you shop around, and go with someone who will work with you and who you feel comfortable with. Most funeral homes are able to give a large discount to assist with the cost, but don't exspect to get a $20,000 funeral for $1,000. Try to look at all your options. You can easily have a visitation and service with a basic casket for $6,000 its all on the casket cost.
My other suggestion would be to have a fundraiser to help with these exspenses.
I hope this helps in some way.