Updating Woes- Your Help is Appreciated!

I own a website that is using an out of date version of wordpress. Recently (I should have seen it coming) code was injected into the site, and tons of invisible ads were put onto the site.

I since went through each page and cleaned out the code, but I realize that I need to update wordpress to protect from such attacks in the future.

The reason why I have yet to do so, is because I have custom code linking wordpress to a number of plugins and databases on my site. This part of the site was set up by a third party, and I would hate to somehow corrupt the site.

I am far from an expert on WordPress’ structure and handling of additional code, so is it likely that an update would overwrite important files?

Finaly, how much do you think it would cost to outsource someone to backup, update, install the latest version with the plugins?

Here is a link to the site: Houston Lawyers

Thanks in advance, I appreciate it!