I have moved my domains from a vps and what I did was to setup a new username from 'manage users' and use the same same 'username' 'password' as per the domain at the vps.
When you add the domain from the 'manage domains' page then by default your root document space begins at "example.com" (your domain name) but you can change this if you wish an set it to public_html like you have under cPanel.
However I would advise against that and, since you are starting with a new host go with the flow and use the default. Then if you need help everyone will know where you are coming from pathwise!
I wrote out my plan of action to follow for each domain so that I did not have to reinvent the wheel each time.
1 FTP old site to PC hard drive
1a Likewise any MySQL dumps.
2 Create user with ftp and ssh, (from Manage Users) with old username and password but no email selected from the drop-down. Edit Quota as needed.
3 Add domain (Manage Domains) using the user created in 2 above from the drop down. (I went the default path as far as the web directory went...again I recommend doing that)
4 Add main email user (Manage Addresses) email@example.com where user is as 2 above.
Select Mbox login (user created in 2 above) from dropdown.
Mailbox name can be same as user name (from 2 above), and password as from 2 above. Create email address.
(That will create a username/password setup as per your main cPanel domain account that you can use in your email client without change-assuming you used mail.example.com under cPanel.)
5 Create email aliases. Same as in step four but use your main email user (from 2 above) in the 'will be delivered...' box and untick 'deliver to this mailbox' since you are creating email aliases.
6 FTP from PC Hard Drive to new location using ftp/ssh (username/password) from 2 above where you use the root web directory of your domain. (For ftp server location use yourdreamhostserver.dreamhost.com. Install any MySQL databases as required.
7 Update the nameservers for your domain. Wait for propagation...