Upgrade Joomla Site from v2 to v3

General information for the website: my hosting provider migrated to a new server, now my old site doesn't work. It needs to be upgraded and properly configured again.
Kind of development: Customization of existing website
Description of every page/module: The website is not huge or updated frequently. It's basically just static marketing and a contact form with some pictures. I don't have a working copy hosted at the moment because it broke when migrating my server.

Here's a glimpse at what it was like: https://web.archive.org/web/20150509021049/http://www.uniquetravelplanners.com/

I can give you direct access to the server which still has all the files and should have a working MySQL database just as before.

I'm guessing it's just some incompatibility between Joomla 2.5 and the version of PHP currently installed or something like that. However, I would really like to upgrade Joomla to the current version with current extensions.
Description of requirements/features: Upgrade to Joomla v3. Working homepage and contact form.
Specific technologies required: Joomla
Extra notes: