This is what I would suggest [you've done some of it already*]:
A. Create an empty new site on the new domain
- create a new empty database* in the new domain [e.g. in
www path may vary.
- download the newest version of WP to your PC
- Using FTP [e.g. filezilla] Upload the WP-files yo the new domain
- open url http://newdomain.com
WP will start the 5 mins setup process.
- Fill in the fields with the required settings for the newdomain.com. NOTE!! Give the same prefix as the old database! You should now have a working site.
- login the newdomain.com and check if things are working
B. Create a back-up of the old website
- using FTP make a back-up files of of the old website on your PC
- make a back-up of the old database!!! Dashboard > Tools > Export
- Choose 'all content' and click 'download exportfile'
An exportfile will be saved onto your PC.
C. Filling the newdomain database with the data from the exportfile.
- dashboard > import > wordpress
- [if required] Install NOW to install the import-utilty
- click 'activate the plugin and run importer'
- choose the exportfile and run the import
You should now have the original CONTENT, not the looks.
D. If all works well technically, not the 'looks', make a backup of the files of the old site using FTP
E. Transferring themes, plug-ins etc
- Use FTP to copy the olddomain site to PC [see backup]
- In FTP open newdomain
- Upload ONLY theme, childtheme, plug-ins and images to the new site
DON'T copy the old wp-config.php and rest of the old files in the root of the site.
You may have to activate the plugins etc in the new domain
- Recreate the old menu / menu-structure in the new sit
Unless I have forgotten something in this list... You should have a complete transfer...
Your site is now ready to be used and tweaked further.
Make sure you make back-ups.
Don't make any changes to a theme itself. Instead make the changes to a childtheme. Should the author of your original theme update the theme, your changes will not be overwritten. Your site with your adaptations will remain intact.
(see: http://codex.wordpress.org/Child_Themes )
Suggestion: use the 'one click childtheme plugin'.