I am re-themeing a very large site. Unfortunately I cannot

Hi I am re-themeing a very large site. Unfortunately I cannot re-theme with a theme from here (I'd like to, but none meet the specs)

But I am looking for some advice on the best way to re-theme this huge site and avoid as many major issues as possible..

I heard that some plugins need to be activated after other plugins and that there is sometimes and order to it.

I have listed which plugins that are currently on the site (I did not build the site, and I have not heard of a few of these plugins).

Can you please tell me which of these should be deactivated to reduce major issues and known conflicts? There are a few that were not active anyway.

Also, if you can please tell me if there is an order to re-activate them so that they will be installed in the correct order to reduce issues and conflicts.

Also, if you can let me know if there are any known issues with any of these, I'd really appreciate it.

Adminer - (not active)
Akismet
All In One SEO Pack
Author Information Widget
BackWPup
Black Studio TinyMCE Widget
Cart66 Importer - (not active)
Cart66 Professional
Embed Iframe
Facebook Comments
Facebook Members
Fixed Social buttons
Google+ Plugin
Google Calendar Events
Google XML Sitemaps - (I deactivated so no problem with duplicate content while I re-theme)
Gravity Forms
Gravity Forms MailChimp Add-On
Hyper Cache
InfiniteWP - Client
Jetpack by WordPress.com - (not active)
MailChimp
Multiple Twitter Widgets
Optimized Dropdown Menus
PHPurchase - (not active)
Pinterest Pin It Button
Portable phpMyAdmin
Redirection
Revision Control
RSS Image Feed
Shareaholic | share buttons, analytics, related posts
Syndicate Out
Theme Authenticity Checker (TAC)
TinyMCE Advanced
TubePress
Under Construction
WP-Mail-SMTP
WP Smush.it
WP Super Cache - (not active)
Yoast Breadcrumbs

Thank you!!!