EA gave everyone who owned Sims 2 on Origin an "Ultimate Collection" earlier this month. EA have now expanded the offer so that everyone can get the game. All you need to do is download Origin, log in, and go to Origin > Redeem Product Code. Type I-LOVE-THE-SIMS in the field and you should now own the game and all the expansions.
Sims 2 is one of my favorite games ever, so I'm downloading the game as I'm typing this. This opportunity may also be the only way to get it digitally if you don't already own it as it's no longer sold normally on Origin, so I would highly recommend everyone to download it if you got even the slightest interest in the game.
Here are the the solutions for probably the two most common issues.
First, my post on how to change resolution: "http://pcgamingwiki.com/wiki/The_Sims_2 This tells you how to make the game run at any resolution you want. The path you want to go to is \Fun with Pets\SP9\TSData\Res\Config"
Another issue that you are likely to have on a modern graphic card are black boxes under Sims. It's the shadows of the Sims that are causing this issue and they can be turned off in the same file you changed resolution in. Search (Ctrl+F) for "option shadows" and under high settings change "boolProp simShadows true" to false. This will turn of the shadows on Sims but lets you keep shadows on objects.