You will need to purchase Snow Leopard in order to be able to download Mavericks or earlier for your computer because whatever was installed by the prior owner is not licensed to you.
You can purchase Snow Leopard through the Apple Store: Mac OS X 10.6 Snow Leopard - Apple Store (U.S.). The price is $19.99 plus tax. You will be sent physical media by mail after placing your order.
After you install Snow Leopard you will have to download and install the Mac OS X 10.6.8 Update Combo v1.1 to update Snow Leopard to 10.6.8 and give you access to the App Store.
Upgrading to Mavericks
You can upgrade to Mavericks from Lion or directly from Snow Leopard. Mavericks can be downloaded from the Mac App Store for FREE.
Upgrading to Mavericks
To upgrade to Mavericks you must have Snow Leopard 10.6.8 or Lion installed. Download Mavericks from the App Store. Sign in using your Apple ID. Mavericks is free. The file is quite large, over 5 GBs, so allow some time to download. It would be preferable to use Ethernet because it is nearly four times faster than wireless.
OS X Mavericks- System Requirements
Macs that can be upgraded to OS X Mavericks
1. iMac (Mid 2007 or newer) - Model Identifier 7,1 or later
2. MacBook (Late 2008 Aluminum, or Early 2009 or newer) - Model Identifier 5,1 or later
3. MacBook Pro (Mid/Late 2007 or newer) - Model Identifier 3,1 or later
4. MacBook Air (Late 2008 or newer) - Model Identifier 2,1 or later
5. Mac mini (Early 2009 or newer) - Model Identifier 3,1 or later
6. Mac Pro (Early 2008 or newer) - Model Identifier 3,1 or later
7. Xserve (Early 2009) - Model Identifier 3,1 or later
To find the model identifier open System Profiler in the Utilities folder. It's displayed in the panel on the right.
Are my applications compatible?
See App Compatibility Table - RoaringApps.
Upgrading to Lion
If your computer does not meet the requirements to install Mavericks, it may still meet 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.
Be sure you install Snow Leopard as follows:
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. Be sure you configure your initial admin account with the exact same
username and password that you used on your old drive. 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.