You can't go to 7 straight from 6.0.
I would take two paths - the first is just upgrading your db and data directories to 6.2, then to 7.0. The intermediary stop shouldn't be too much of a pain, just take care to do all necessary data cleanup for your 6.0 -> 6.2 step as well as the 6.2 -> 7.0 step. This means backing up your DB & data directory so you can roll back, fix problems and try upgrade again, repeating until you get a clean upgrade.
The code will take a different path. 6.x themes need to be rewritten for 7 anyway, so just peel that one off and pursue the rewrite separately.
The other plugins all face significant changes to migrate to 6.1 and 6.2 and 7.0. With so many changes involved, you may or may not find it easier to just rewrite them for 7.0 right off the bat. It's hard to say not knowing what you've done with your 6.0 code to know which is better.
A word going forward - don't let yourself get so far behind Liferay releases. With each release liferay usually has some sort of plan for going from the last version to the next, but as you can see you're now looking at possibly four hops to get this done or bypassing to get to the latest version. When you keep up with Liferay releases, the upgrade steps are much easier to handle.
