Why do you need 301 redirects from an old site to a new one? Are there a certain amount of backlinks and internal links one should have as well?
301 redirects are instrumental in making sure that any "link juice" that exists for your site is not totally lost when you either transfer domains or reorganize your site and take down any existing pages. When Google and other search engines rank your site, they look at several key factors in order to show the visitor the most relavent result (Keep in mind that Google is a service and they want to make sure their customers are happy).
Factors that Search Engines Consider
301 redirects help maintain any backlinks that are currently set-up for your site.
A backlink is any link on the web that properly points to your site. For instance, if you sold Cat Food on your website www.catfood.com and a magazine was reviewing your site they might put a link on their site for Cat Food At Great Pricing. The phrase "cat food at great pricing" is called the Anchor Text and is what visitors would click on in order to go to your site.
Now, let's say that for whatever reason you wanted to move your site to www.catfood.net, you would have to contact all of the sites that have backlinks point to your ".com" domain and ask them to repoint them to ".net". This is a tedious process which often yield luke warm results. However, if you set-up a 301 redirect that automatically sends visitors to the correct page, you retain most of the value from the link on the magazine's website, while also making sure that visitors get to your site. When setting up 301 redirects, make sure to do as best you can in sending them to the right page, and not just the home page. For instance, if you had a page on your site for "Wet Cat Food" don't simply just redirect them to the home page, send them to the new page for "Wet Cat Food."
SEOMoz has a lot more in-depth information on 301 Redirects
See how the anchor text is 301 Redirects and not SEOMoz. This tells search engines that the site is being endorsed for "301 Redirects" so that when someone performs a search for that phrase, SEOMoz will have more credibility. When trying to obtain backlinks consider the keywords and phrases you want to rank well for and ask to have those be the anchor text on other websites.
The simple answer is the more the better, however consider the site that is backlinking to you. One backlink from a highly reputable site is worth a lot more than ten backlinks from "no-name" sites. And beware of companies offering to get your 100s of backlinks for cheap, as they most likely will submit your site to link farms and perform other "black hat SEO practices" which may boost your site at first, but once the search engines find out what is happening (and they always do) your site will immediately disappear from search results and may be banned, which is very difficult to come back from.
In general, always set up 301 redirects when you can and setting up backlinks to your site will help organic rankings, the more QUALITY backlinks to your site, the better.
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