@MsSaintsAngel Adding a number of lots to a world can definitely cause the save to eat up more RAM than usual, whether those lots are residential or not. Having too many sims in a world can also drive up memory use, although what qualifies as "too many" will depend on the world and how many packs are installed. I'd still be interested to know how much RAM TS3 is using when you run this particular save, since there are other causes of Error 12 besides the game running out of memory.
If you move your family to a new world though, it's not going to matter what you left behind in the old one. It sounds like you're trying to use the in-game move function? It's much better to just save your sims to the bin and place them in a new save instead. The result is the same—you lose all the data from the old world and start fresh, with your sims knowing no one—but this keeps data from the first world from being transferred to the second. So the new save won't be corrupted before you start, and it will likely use a bit less memory too.
As for the helpful mods, you've already found several of them. Saver doesn't do anything by itself; it's just a timer that reminds you to save, if you tend to forget. ErrorTrap and Overwatch are great, as is MasterController for its "reset everything" function. (Click on City Hall, NRaas > MC > Town Options > Reset Everything.) In fact, you may want to do this in your current save, to see if it helps with the Error 12s. People with long-running saves tend to run this every few sim-weeks just for the overall health of the town.
If your sims travel at all, you should also install Traveler, which replaces the default, and very broken, travel transition with a much more stable version. It also has a number of extra options to play with, but you can leave the settings on default and still get the benefits of a more stable travel function.
The other two mods that can significantly improve the way TS3 runs are Register and Traffic. Traffic prevents the spawning of extraneous vehicles, both normal ones and things like food trucks. Overwatch cleans up the excess on its nightly runs, but sometimes that's not fast enough; I've heard stories of hundreds or even thousands of vehicles being created in a single day. Again, the default options work just fine.
Register controls service and role sims, including stray animals. Sometimes the game will spawn too many, which will of course drag down performance. On that note, you can check the resident and homeless population by clicking on City Hall, NRaas > MasterController > Demographics > Population > (x out the filter). The homeless population, which will include all service sims (maids, repair people, babysitters, that kind of thing) as well as in all likelihood most role sims (the ones that staff a role giving object, like a cash register or velvet rope at a club), isn't important unless it's extremely high. The resident population is more important, although as said before, how many is too many will depend on the world.
If you have Island Paradise installed, you may want GoHere for its ability to disable boat routing for sims; some worlds don't work well with boats. If you have Supernatural, you may want Hybrid for a couple of fixes it provides, although that's less about the game running well than details like being able to properly edit werewolves' wolf form (I think; I still haven't installed Supernatural). But most of the other mods are about adding features to the game, not cleaning it up.
Fiddling with virtual memory won't help TS3 run any better, unfortunately. The game just isn't programmed to use it. I'm sure it helps other players who like to multitask and maybe only have 8 GB RAM installed, since other apps will take advantage, but I doubt your system is running out of memory overall.
Finally, on the graphics settings, the only two that really matter are water and high detail lots. You should be able to max out all the others. But high detail lots determines how many lots are loaded at any given time, and a high number will take a lot of memory. Water is more about VRAM, at least I think, but I keep it low except for the rare occasion when I'm taking scenery screenshots.