One option is to use Firefox, which is still being updated for 10.6. Link below.
Firefox
Your upgrade options are 10.7, 10.8, or 10.11. Since 10.7 and probably 10.8 are no longer being supported, I'd suggest 10.11.
Check to make sure your applications are compatible. PowerPC applications are no longer supported after 10.6.
Application Compatibility
Applications Compatibility (2)
El Capitan 10.11 Compatibility information
Do a backup before installing, preferable 2 backups on 2 different drives.
One option is to create a new partition (~30- 50 GB), install the new OS, and ‘test drive’ it. If you like/don’t like it it, you can then remove the partition. Do a backup before you do anything. By doing this, if you don’t like it you won’t have to go though the revert process.
Open Disk Utility, select your hard drive (step 1), then the Partition tab (step 2), and select the partition. Using the /// at the bottom move it up (step 3) until the size box decrease by about 50 GB. Select the newly created space and hit the + button (step 4). Name it something and select Mac OS Extended (Journaled) as the format (step 5). Then hit the Apply button(step 6). Download the installer from the App Store and when it starts, point it at the new partition. You might want to make a copy of the installer outside the Applications folder to avoid having to re-download it in the future. Once installed, go to System Preferences/Startup Disk, select the new partition and reboot. Test away.