Unless you downloaded one of the earlier operating systems, they have been removed from the App Store. I believe your iMac is a late 2009 so it is capable of running up to Mac OS X Sierra.
Best option would be to upgrade to OS X.11 El Capitan which is fast on older Macs. Also depending how much memory the iMac has, consider upgrading to 8GB. Read this relating to El Capitan, and remember back everything up first:-
If your iMac still has the original mechanical hard drive, the newer versions of MacOS will run a bit slower than what you're used to on Snow Leopard. After putting an SSD into my Mid 2010 iMac 11,3, it felt like a brand new Mac on OS X El Capitan or MacOS Sierra - so I can definitely recommend this upgrade to modernize an older iMac.
You will need to update to OS X El Capitan first as you're on Snow Leopard, then MacOS Sierra if you want the latest version (and most current app support). If you're unsure about how it will perform, you can create a second partition and install onto that instead of updating your main one. Note that if you're still using old PowerPC apps, those will stop working in versions after Snow Leopard.