Anything that's in a bank account should have beneficiaries on it. Same with life insurance. This way the money goes to the beneficiaries directly without probate and the need for a lawyer and legal fees. Assuming that your father isn't alive or your parents are divorced, that should probably be you and any brothers and sisters you may have. You (or one of your siblings if you have any) should get your mother to sign a power of attorney form, so one of you can do it if it hasn't already been done. It all has to be done before she dies.
You are going to need money to pay for her funeral, and depending on your religion and/or what type of funeral it will be, it can easily cost more than $10,000. I would suggest asking your mother to write you a check for enough money to cover the funeral expenses plus enough for anything else that might come up. Otherwise, if you don't have the money yourself, you might have to pay for it on a credit card until you get the money from your mother's accounts.
If there are siblings, whoever is going to be in charge of things should keep a spreadsheet to track the check from your mother and any money paid to the estate, etc., along with expenses. This way, you can keep track of any shared money and distribute it equally once all of the expenses are taken care of. You will also most likely need to file an income tax return.
If there is any money that will be shared equally, make sure enough is set aside for taxes, a grave stone, etc., which might not get purchased right away. Of course, if everything is going to you, you probably don't need to keep track of things like that.
As far as bills, find out from your mother who she owes (doctors, credit cards, etc.). Also she might have recurring bills, magazine subscriptions, etc., that you would want to cancel and maybe get a pro-rated refund.
I would suggest taking out one or more life insurance policies. These companies are crooks that prey on poor people by charging them high premiums for a small benefit, but they are very worthwhile if you know that someone is going to die. I thought of this when my mother was dying because I got an advertisement in the mail. The people I spoke to over the phone thought I must be a horrible person because I was asking details about how long it takes to get the policy in place because my mother was probably going to die within a week. But I wasn't being cruel at all, it's not like I was killing my mother to make money - I would rather that my mother didn't die, but since it was inevitable there was no reason not to make some money from these crooks. Keep in mind that the death benefit is limited in the 1st year. I think I paid about $50 for one month's premium, sent in the application by Express Mail, it was processed a few days before she died, and I made about $1,000 whgich I shared with my brother even though jI was only able to put my name on the policy.
I don't know much about a home, you might want to get legal advice or find out from someone who went through this. But you should make sure that the mortgage gets paid.
Went through this with my mother, who didn't own a home or car, so we were able to do everything without a lawyer. This worked because it was just me and my brother splitting everything equally, and there were no disputes or issues with people not being trusted. Actually the only dispute was that I ended up living in my mother's apartment and there was a lot of stuff from her and our father that I wanted to get rid of, and I wanted him to take more stuff than he did.