I recommend unpublishing all non-core CB plugins, unpublishing all integrations with CB (K2, Kunena, CBSubs system plugins, admin nav module, etc..). Once done install CB 2.x. This should avoid any conflicts that could prevent migration from working correctly. Joomla menu items aren't migrated and don't need to be re-created; just edit them and fix their menu type since that assignment was broken in CB 1.x. Your userlists should be fine, but if not please detail what didn't migrate.
If your custom template is a CB template then it won't be compatible with CB 2.x as we've completely redone all of the frontend HTML and are using Bootstrap 3 in CB 2.x.
CB plugins do not upgrade automatically on install of CB. Only core plugins included with CB do. For the others you need to use the below chart.
www.joomlapolis.com/cb-20-addon-status
There's also several videos below for CB 2.x
www.youtube.com/playlist?list=PLp0puRITgC7PuyzPsMUECDI46VE7IFSAX
The below video also describes what to expect.
We've also a CB 2.0 Primer Book below to help detail CB 2.x usage.
www.joomlapolis.com/component/docman/doc_details/753-cb-20-primer-book-101
It's also strongly recommended to upgrade a clone of your site so you know exactly what to expect for your live upgrade.