Safari on OS X 10.6.8

I would not upgrade from Snow Leopard unless you need to. In that case you can only upgrade to 10.7.5 Lion. But this will not fix your current problem. I would suggest that you do a scratch reinstall of Snow Leopard:

Clean Install of Snow Leopard

Be sure to make a backup first because the following procedure will erase

the drive and everything on it.

1. Boot the computer using the Snow Leopard Installer Disc or the Disc 1 that came

with your computer. Insert the disc into the optical drive and restart the computer.

After the chime press and hold down the "C" key. Release the key when you see

a small spinning gear appear below the dark gray Apple logo.

2. After the installer loads select your language and click on the Continue

button. When the menu bar appears select Disk Utility from the Utilities menu.

After DU loads select the hard drive entry from the left side list (mfgr.'s ID and drive

size.) Click on the Partition tab in the DU main window. Set the number of

partitions to one (1) from the Partitions drop down menu, click on Options button

and select GUID, click on OK, then set the format type to MacOS Extended

(Journaled, if supported), then click on the Apply button.

3. When the formatting has completed quit DU and return to the installer. Proceed

with the OS X installation and follow the directions included with the installer.

4. When the installation has completed your computer will Restart into the Setup

Assistant. After you finish Setup Assistant will complete the installation after which

you will be running a fresh install of OS X. You can now begin the update process

by opening Software Update and installing all recommended updates to bring your

installation current.

Download and install Mac OS X 10.6.8 Update Combo v1.1.

Once you complete the above you should find things much snappier. You can now consider if you wish to upgrade:

Upgrading to Lion

Your computer does not meet the requirements to install Mavericks, it still meets the requirements to install Lion.

You can purchase Lion at the Online Apple Store. The cost is $19.99 (as it was before) plus tax. It's a download. You will get an email containing a redemption code that you then use at the Mac App Store to download Lion. Save a copy of that installer to your Downloads folder because the installer deletes itself at the end of the installation.

Lion System Requirements

1. Mac computer with an Intel Core 2 Duo, Core i3, Core i5, Core i7,

or Xeon processor

2. 2GB of memory

3. OS X v10.6.6 or later (v10.6.8 recommended)

4. 7GB of available space

5. Some features require an Apple ID; terms apply.