Hi Spencer and welcome to Able2know.
I haven't been in your situation but I know that my own mother has, for her father.
My suggestion to you would be, assuming your mother is still lucid, to ask her what she would like. I know that sounds odd, but your mother, I am sure, realizes that her situation is dire. But she's also got very little control over things going on in her life (after all, if she were in control, she'd just get herself better), so it might be a comfort, odd as it sounds, for her to take some control of her funeral. I don't mean the actual calling, pricing and other arrangements, I mean just generic types of questions such as -
Mom, I know this may be a difficult subject and if you don't want to talk about it, I understand. But I was wondering if you had any thoughts as to the arrangements. (I don't think you need to spell it out; I'm sure she'll know which arrangements you're talking about)
If she's receptive, ask but don't overdo if she becomes tired, upset or irritable, such as -
Would you prefer a particular cemetary? Type of casket? Type of service? Would you rather be cremated? If so, where would you like your ashes to be sprinkled? Do you want a marker? If so, what do you want it to look like and say? I want to do what you like, whatever it is.
And then see what she says. She might want a plain casket, or a fancy one, or just to be cremated. Also, it's possible that she's already made some arrangements and has been waiting for you (or someone) to ask her about them.
But what if she says nothing, or is incapable of making these decisions?
If that's the case, then there are a few things to take into consideration:
(1) what does your faith (if you have one) say about such things? Me, I'm Jewish; we're required to have plain caskets so that decision is essentially made for us. Your traditions might dictate likewise.
(2) if not your faith, does your family have traditions or customs? Perhaps everyone is buried in a particular cemetary, or holds a wake in a particular manner. Ask your mother's syblings if they are still alive, or her friends, they might know.
(3) is your mother or your father a veteran? A union member? If so, certain benefits might attach. A veteran can buried (here in the US; I don't know where you live) in Arlington Nat'l Cemetary. If the veteran is buried there, the wife can be, too. As for a union membership, I recall my great-aunt was a union member and her union took care of some of the expenses. It pays to ask.
(4) you can also ask your sister, assuming she is old enough to understand and participate in such things.
What do you think Mom wants? She (your sister) might be able to help out in this area.
Since your mother is ill, you may have some time to think about this and coordinate it. It may seem morbid to be shopping around, but consider the fact that it will be easier to do this now rather than later, when your mother has already passed and you are under some time pressures. If you can find the time, to break away from work and from care, to visit some funeral homes and do some pricing, it will be a great help to you later. Also contact the Better Business Bureau in your area (again, I'm assuming that you are an American), as, unfortunately, funeral home directors can sometimes be unscrupulous, and prey upon grieving loved ones who are not thinking about money.
It is not a bad thing to not have the most expensive funeral, casket and tombstone. It is no shame and it does not mean that you loved her any less.
Funerals, etc. can be costly. You're right to think of your sister's financial future. Now is the time to start doing the legwork, if you're emotionally up to it. Bring a friend, someone who can be objective and can ask the tough questions, or your wife or girlfriend if applicable. It will help to have someone to bounce this off of.
As for handling the estate, get into contact with your mother's lawyer and find out what being the executor (I assume that's the situation) means. That's if there's a will. If there is no will, then you are called the administrator of the estate and of course there is no lawyer but that does not mean that you cannot hire one. As with the funerary arrangements, shop around and also ask friends about who they can recommend. You can handle the estate yourself, but it is work and you may or may not be emotionally up for it. Here is an article on being an executor:
http://www.usatoday.com/money/perfi/columnist/block/0016.htm
And my heart goes out to you, it must be a difficult time.