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You will want to do this on a local host first to insure you can upgrade your main site.
Also before upgrading you will want to remove any unnecessary modules and make sure you can find replacements for your current modules.
You will want to disable all of your modules except system before you upgrade so you don't have any incompatible modules active when you do the upgrade.
Once you upgrade check your theme for compatibility and once your theme is running smoothly then try upgrading your modules one by one and getting them to work on your site.
You may find some of your modules have totally new replacements for them and others not. 2.0.13 is pretty old so you may find you can not replace some of your modules with upgrades and have to go to different modules or not be able to use that module.
All depends on what modules you have installed. Feel free to post what modules and versions you have so we can better help you with your migration.
Rodney