Lianne,
First let me say how sorry I am to hear about your ailing cat. I know from experience how difficult it is to see you pet's health decline, and the time and effort it takes to care for an elderly pet who is sick.
I contacted the Belleview Pet Crematory, which is close to The Villages. I suspect if you go through them directly, rather than through a veterinarian that the cost will not be as high (that is a guess, not a fact). They have two kinds of cremations for pets. A private cremation, meaning only your pet is cremated and you receive the ashes in an urn, costs $160. A communal cremation costing $60 is done with several pets all at once, and the ashes are scattered on a horse farm. The cremation is usually done the same day the pet is received. Their phone number is 352-307-2256 and are located at 10505 Southeast 36th Avenue in Belleview.
If you choose to forego the cremation, your vet can euthanize your cat and dispose of the body. "Dispose" means that your cat will be placed in a thick plastic trash bag which will go in the trash.
Or, you can let your cat die naturally, wrap the cat in several plastic trash bags and dispose of the body in your regular trash pick up. However, if the cat is suffering, your vet can provide pain medication and sedatives.
This link discusses how to care for a dying cat and may be helpful:
http://www.ehow.com/how_2083410_care-dying-cat.html