|Netbooks weren't built for gaming, so it may not run well for long once you get it installed. Netbooks are intended for basic web browsing and office documents (which explains their smaller size and lack of optical drives), so you may be better off getting a laptop, although heat will be an issue on both when it comes to gaming.|
If you're going to download it legally online, you'll have to buy it again. EA Games doesn't offer it free just because Sims 3 is out.
You could consider buying an external CD/DVD drive that plugs into a USB port on your Netbook. http://www.newegg.com/Store/SubCate...
After installed, you could download a legal "No-CD" patch from http://www.gamecopyworld.com/
They aren't always perfect, but worth a shot. Some patches I've tried didn't include game music or allow multi-player, but others worked fine. I downloaded the No-CD patch for Sims 2 Open For Business and it works flawlessly.
Apologies if I don't respond to your reply immediately. I don't check this site daily, but you're welcome to PM me as a reminder.