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_First of all I would like to know why want to get your website bookmarked in social bookmarking sites. Unless there is a greater possibility of gaining some visitors, I do not think it is worth your time. Do not chase the algo, rather chase the visitors. _

I'd keep the old site live and build links to it. This means you have an actual live and complete website that other sites are more likely to link to, as apposed to a coming soon page. It gives you the option to build deep links to pages on the site. You can 301 redirect if URLs change on the new site. It also means you can start link building now, not have to wait 3 months for the new site to go live. As you know there is always a delay between the start of a link building campaign, and the results. Hope this is more helpful.