Dad is 81 and starting to decline mentally and physically. Mom is 79 in still in good health. Mom is starting to have difficulty caring for Dad, and would like to sell and move Dad to a nursing home. They have the house and everything accumulated over the years. Where would she begin?
As for the house, don't start moving just yet. Where is your mom going to go? She needs to figure out where she's going to live.
While these plans are being made you can begin to go through the house. My brother and I sold our parent's house and we started with anything that could be thrown out like tax returns from 1958. My mom had old hat boxes from the '60's that we pitched. My dad's tie rack from before he retired. Anything that you can look at and see that it's not necessary to keep no question about it can go.
You just find a starting point and go from there. We hired a dumpster that sat in my parent's driveway and we just made about a zillion trips to that thing over the course of the weeks. When it was filled we called them and had them empty it and we started with another one. We designated an area for things we weren't sure about such as old records and files and we had another area designated for things we'd come across that someone might want to keep. During this process we also had people coming into the house to work on the kitchen or the basement. My dad left town while we did this and it was a blessing that he wasn't there. You might want to get your dad moved into a nursing home prior to all of this. It's pure chaos.
Once you've gotten a lot of stuff thrown away, once you've winnowed down the piles of stuff you're not sure about, call a real estate agent. I think agents are pushy and obnoxious but they're a necessary evil. Ours wanted everything done yesterday and didn't care that my brother and I both worked and we couldn't jump when she snapped her fingers but over a pretty short period of time she got the house looking good and ready to sell. It was a tremendous amount of work but it got done.
So just start out small and chip away at it a little at a time. It will be emotional and stressful but just keep at it and it'll all get done.
Second, where do you all start? What we did was this. Each of us three kids determined what furniture and goods we could take and hired vans to move out big pieces. I boxed up books, knicknacks, clothes, etc and made a couple of dozen trips to Goodwill. I put some stuff out at the curb and people driving by delighted in new treasures. We called Goodwill to pick up the rest of the furniture. We shredded the tax returns that went back to 1958. The pictures are still in boxes in my spare bedroom. Mom was already in a nh, so she wasn't around to fuss.
If that sounds like a good idea, your parents could move before they start downsizing the house [if they are financially able].... then move in whatever furniture they need and later come back to the house to take care whatever is left to do.
Your Mom sounds like a very smart woman, knowing it is time to doing something. My Mom is the one digging in her heels as my Dad wants to go to independent living as their large home is too much for them.
As for getting a licensed Realtor check with your friends to see if they had recently bought/sold a house.... or go to the Open Houses on Sunday in your neighborhood and see if you get a good vibe from the Realtor at the Open House. Too bad you don't live nearby, I know a really nice agent who is also an Elder Care advocate.