I think that's a very personal question. I think perhaps you should investigate BOTH possibilities.
Start systematically going through your house, closet by closet. Don't start a project until you can finish it. Tear apart a closet, down to EMPTY. Then decide what that closet really should be used for. Let's say it's the front entrance/hall closet. Perhaps ONLY jackets should be in there. Make piles for each family member, so they can see what they have. Then either you/or they decide what's really used...what fits, what's torn/broken/stained, etc. Then make new piles accordingly...keep (goes back in the closet), donate/sell or garbage. Do this with EVERY place in your house. I try to do this every year or two - like the basement this year, the closets the next.
As for the kids, depending on how old they are, they should be able to do the same with their rooms (with help). Once my kids started to understand that their "stuff" was going into their rooms or the playroom ONLY, they didn't want to save as much. We explained that it's much easier to keep their rooms clean when there was less to clutter it up or get in their way.
We also started scrapbooks and keepsake boxes to "save" their favorite arts n crafts projects, photos and other keepsakes. I break them out 2-3 times a year to have the kids purge their rooms and decide what they REALLY want to keep.
Yard sales can be a lot of time and effort. When we had things we KNEW would make money, like all the baby gear or big household items, we did it. Otherwise all the clothes, cookbooks, baby bottles, etc. just went to Good Will or a women's shelter in our area. This odds and ends types of stuff gets donated MONTHLY. We just have a bag in the garage where our "old" (as in just bought a new coffee maker, so the old one goes in) or unused things go. We have a scheduled pick up (which helps me keep purging).
After you have cleaned out and organized everything where it really SHOULD be, then check out your house. Is it meeting your needs or is your house too small for the important things your family really wants & needs?
If you decide that you need to move/add on to your house, at least everything is already looking nice and properly stored! So now you'll know what you REALLY need...more storage? Bigger kitchen? Bigger family room?
I hope this helps