The specs are excellent for Sims 3, even on ultra settings (with the usual caveat that the game engine doesn't handle maxing out water and high-detail lots no matter how good your system is). I don't know exactly how you play, but at the very least, it's definitely best practice to start by running the game on your new system with none of your current content.
Before you do anything else, make sure your in-game framerates are capped to the refresh rate of your monitor. Your graphics card is capable of generating fps into the hundreds if not limited, and that's bad for the health and lifespan of the card. You can try the built-in Nvidia Control Panel first, and Nvidia Inspector (free download) if CP doesn't work. It never works in windowed mode, so if you use that, or switch between fullscreen and windowed, you'll need a different app. Here are excellent instructions for both tools:
https://forums.thesims.com/en_US/discussion/comment/16540301/#Comment_16540301
To see fps, bring up the cheats console (ctrl-shift-C) and enter "fps on" without quotes. The number will appear in the upper right corner of your screen, and it should never exceed your monitor's refresh rate. ("fps off" makes it go away.) There are other apps you can use, if CP and Inspector aren't working, but try these first.
Once you've confirmed fps is capped, you can start downloading mods and custom content. The basic mod list for good performance and error prevention is all from NRaas: ErrorTrap, Overwatch, MasterController, Traveler, Register, and Traffic. As far as other mods go, that depends on your playstyle and what functions you're used to having available.
As for custom content, it's best to check it out, both in the launcher and in game, before it gets anywhere near your saves. Install just a few items at a time, scroll through the launcher to make sure nothing unexpected has installed itself, and then use the cc in-game in a test save to make sure it works as intended. If you do find bad cc, cleaning it out right away will save you a massive headache later.
Once you have a working game folder, and before you add your existing content, it's a good idea to back up the folder on your secondary drive. That way, if something goes wrong with your game folder later, you can swap out a fresh copy instead of having to rebuild it from scratch.
You can move your saves, builds, saved households and sims, etc. to your new computer either with an external hard drive or USB stick, or by uploading the files to cloud storage and downloading them on your new computer. There are plenty of filehosting sites that offer a couple GB of free storage, or you could sign into your Windows account and use OneDrive—just make sure to disable auto cloud syncing. Here's a list of everything you'll find in your game folder, in case there's anything else you want to keep:
https://sims3.crinrict.com/en/2011/01/faq-user-files.html
