Are there any risks installing the latest versions of safari? What do I need to do to prepare?

It depends on which OS X is installed on your Mac.

Click your Apple  top left in your screen.

From the drop down menu click: About This Mac

Make sure the Overview tab is selected.

Which OS X version do you see?

The latest Safari version available is 9.1 but that is only for OS X 10.11 El Capitan.

In order to have the latest security provided by Apple possible, yes but see the specs below to make sure your Mac meets El Capitan requirements.

General Requirements

• OS X v10.6.8 or later
• 2GB of memory
• 8.8GB of available storage
• Some features require an Apple ID; terms apply.
• Some features require a compatible Internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen, choose About This Mac, then choose More Info. These Mac models are compatible with OS X El Capitan:

• MacBook (Early 2015)
• MacBook (Late 2008 Aluminum, or Early 2009 or newer)
• MacBook Pro (Mid/Late 2007 or newer)
• MacBook Air (Late 2008 or newer)
• Mac mini (Early 2009 or newer)
• iMac (Mid 2007 or newer)
• Mac Pro (Early 2008 or newer)
• Xserve (Early 2009)

OS X El Capitan - Technical Specifications

About El Capitan security here > About System Integrity Protection on your Mac

If you decide to upgrade, make sure to backup all your important data first !!!!

You can easily find storage and memory details by clicking on the Apple logo in the upper left of your screen and selecting "About This Mac". On the first popup window that opens you will some general details about your Mac. You can then click on the tab at the top labelled "Storage" for the storage details.

Are there any risks installing the latest versions of safari?

There are risks with not updating, because only the most recent versions of OS X contain the most recent protections against unauthorized alteration or malicious interference. In other words remaining with outdated operating system and Internet browser versions exposes your Mac to a greater number of threats than keeping it up to date.

... What do I need to do to prepare?

Back up your Mac, if you have not done so already. To learn how to do that read https://www.apple.com/support/backup/. To learn how to use Time Machine read Use Time Machine to back up or restore your Mac. Apple makes those recommendations in their applicable Support document: Upgrade to OS X El Capitan - Apple Support.