Brother lives close, I'm in TX. They have collections of LOTS OF THINGS. For the most part, it is very organized with boxes and notes on the boxes of what is inside.... but they're EVERYWHERE!!!!! My brother is a self-contractor, so if he doesn't work, he doesn't get paid. I'm in Texas, so I would have to fly back and forth frequently (which cannot happen that often!). Antique dealers would love to get their sticky fingers on some of the goods and offer MAYBE ten cents on the dollar!! Crooks! Even getting an Appraiser just to look things over for their best opinion of value is approximately $100 +/- per HOUR!! We need some specialists for specialty items. What are we going to have to do?? This is a 4-bedroom, 3-bath home, and every room, even the closets and bathrooms are FULL!!!!
If there are true antiques or a group of collectibles, you can take photos of them with your phone and email to the bigger auction houses to gauge interest in their including them in a future sale. If they are valuable or are of interest, the houses will arrange for pick up & storage till their sale which tend to be done by categories.
But what often happens is that most of what family has is not of the quality or provenance to go to auction. Because of all the "storage" & antiques TV shows, folks think what they have is special. The TV shows are staged reality. It's rare that an old bed is a true Mallard; or the lamp a true Tiffany…..
You mentioned there are oodles of boxes of "things". If these are filled with ephemera or printed materials (books, cards, certificates, games, etc) & if they have not been stored property - like in acid free boxes or slipcases or Ziplocs - a lot of places won't take them as they have mold or mildew or other tiny varmints that pose issues for inventory. Almost all of FL is coastal with humidity issues that make this even worse too. I'm in New Orleans and volunteered for years at a really big rummage sale and we would jettison any books and fabric items with any moldy smell or tinge as to be on the safe side.
If you & bro cannot do what is needed to sort & edit what is in the house, you probably have no choice but to either pay for a professional to establish worth OR to have a picker go through the house and pay you about 20% or maybe 30% on what they think the value is for select items. The consignment shops usually have a list of folks who bring them inventory. What often is a good idea is to visit several consignment shops and find 1 or 2 that has inventory similar to the stuff in your parents place and have them give you the names of the pickers for those items.
If you need to divest the whole house, they will know someone who can do an estate sale. These usually run on commission (maybe 30%) plus expenses or a set minimum.
If under 5K/10K in value of stuff, it might be hard to find anyone interested btw.