yes, you can use Snow Leopard, 10.6.8 on these Macs and even 10.6.4. 10.6.8 is better optimized and has access to the Mac App Store for the few applications that still have older versions that run on it.
Browsers by Mac operating system - Apple Community
tells you what browsers exist for each Mac OS.
Your 2009 Mac can upgrade up to High Sierra if it is a Late 2009 according to Apple menu -> About This Mac.
Otherwise, you will only be able to use up to El Capitan.
A separate partition with Disk utility can be formatted to install a newer operating system, or external drive. Keep in mind High Sierra will format APFS for solid state/flash drive booting, which is not visible to Sierra or older systems while booted from the older system. Firewire drives are available from http://www.macsales.com/ which will work with your Mac faster than USB.
Your Mac is too old for Thunderbolt.
If the Mac has the original internal hard drive, see if an authorized service center may be willing to swap out the hard drive. This is not a user accessible internal drive.
Use 10.6.3 retail disk which looks like
to boot off the Option key to install Snow Leopard if not already present on your Mac. It does not say dropin, oem, or update. 10.6.4 system specific discs will not work with 2009 iMac. March 15, 2010 or later Macs come with a system specific 10.6 installer disc up till July 22, 2011. At that point system restore was built-in for internet restore.
The advantage of Snow Leopard is compatibility with Appleworks, and other software that works both on PowerPC and Intel Macs in Mac OS X thanks to Rosetta. Snow Leopard server can also do this in virtualization on later Mac OS versions with Parallels, but all versions of the Snow Leopard CD are difficult to find at this present time if you don't already have them.