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From Marketing point of view the existence of two different accounts is proper approach. Wedding has separate niche and therefore must have a separate account, it will be not correct to put wedding content into business account. Business account is full of information dedicated to your organisation, etc. Swamping it with wedding pictures is neither proper nor recommended. When there is a separate wedding account you can upload there wedding info, advices, pictures, share ideas of design, interior, wedding help articles. So it is great to directly target for people from the very wedding account. Business account must share info of your services, how you help brand development and there is no use to place any other info on business account.

You must understand what Penguin is AntiWebSpam filter. You must control backlink profile of your site. Your profile must looking naturally. Not only your targeted keywords as anchor texts, not only backlinks on your homepage. For understanding structure of your backlink profile you can use Majestic SEO or Ahrefs (OSE on my opinion not perfect). And often after checking backlink profile I clearly understand what is wrong.

You can build your site on clear HTML but it solution is from past century and it very unproductive way. If question is about choice of CMS - big count of  CMS  is SEO friendly, you not must select Wordpress only.

Better setup your blog on same domain.

Example

http://www.bridalhotspot.co.uk  - Magento

http://www.bridalhotspot.co.uk/blog/ - Wordpress

Updates on blog - new post every 2-3 days. For your market it not hard because you can post news not only about your own clothing but about celebrity wedding etc.

Another possible way is adding your site in Google Webmaster Tools and submit your sitemap.xml in Optimization->Sitemaps section. You will see count of submitted urls and indexed urls.

Wordpress is more user friendly (my opinion).

You not will see big difference in SEO between Wordpress and Joomla.

Example of big site based on Worpdress - http://www.smashingmagazine.com/  - Alexa Rank - 1159

For simple tasks you can use http://www.iwriter.com/ .

I try to setup http://www.seopanel.in/ on server few times. Basic package have pure
functionality and have bugs. For more advanced functionality you must to buy plugins, not very expensive but I not try to do it.