Installing Sims 3 via original discs still works and runs fine. You do need an external dvd drive to install.

If you have Origin installed, login to turn off Game Updates for Sims 3. Or Origin will try to take over your disc installation.
Turn off game updates for Sims 3 in Origin -
Login to Origin > Application Settings > Automatic Game Updates (Under Client Update section) and switch off automatic game updates.
~ If Uninstall/Reinstall:Uninstall the game, run
Ccleaner or similar registry cleaner. This cleans the game out of the registry and gets rid of temp files that get left by uninstalling the program.
~ Installing Game:Start with installing base game. Then install the
Sims 3 Patch Downloader from MTS.
Install the rest of the expansions in order of release. Check
this article from EA Help that lists packs in order of release or see spoiler below. - If installing from disc, It's recommended installing expansions and stuff packs in the order they were released.
From oldest to newest:
The Sims 3
The Sims 3: World Adventures
The Sims 3: High-End Loft Stuff
The Sims 3: Ambitions
The Sims 3: Fast Lane Stuff
The Sims 3: Late Night
The Sims 3: Outdoor Living Stuff
The Sims 3: Generations (May 31, 2011)
The Sims 3: Town Life Stuff
The Sims 3: Pets
The Sims 3: Master Suite
The Sims 3: Showtime
The Sims 3: Katy Perry's Sweet Treats Stuff
The Sims 3: Diesel Stuff
The Sims 3: Supernatural
The Sims 3: Seasons
The Sims 3: 70's, 80's & 90's Stuff
The Sims 3: University Life
The Sims 3: Island Paradise
The Sims 3: Movie Stuff
The Sims 3: Into the Future
~ Playing the Game:Use Nraas
NoCD to play without the dvd in the drive.
It's a mod that allows you to run the game on your computer without having the disc. It's disables the disc authorization.
~ White List the Game in Antivirus Program:There have been reports of problems with programs getting messed with by antivirus programs. To help prevent that from happening. You may want to white list Sims 3. With there being several different antivirus programs you may need to search on how to white list Sims 3 in your specific antivirus program.