Hi,To migrate WordPress you have to follow these steps.
1.Download files from the existing server.
2.Download SQL file from the phpmyadmin and make a backup of it.
3.Open the SQL file using notepad or some other editor.
4.Find your old site path and replace it with newsite path
5.Now import the SQL file to your newsite database
6.Update your wp-config file
7.Now login to WP-admin and update the permalinks.
By this way you can update all your internal links of the website.You need not update them seperately.The only links you have update is the links in php files.