I am trying to download my website on to my system since i am moving servers. I tried to download the full backup using cpanel but the size of the file is 610 MB and since i have a slow connection, it means me downloading the file the whole night. While i dont mind doing that, the connection has broken thrice (once when i had downloaded 517 MB). So i have decided to download it bit by bit. I would like to know what files i will have to download...i can think of just two...the public html folder and my database..is that it? or should i be downloading any other files?
You need your public_html, databases and any mail you on the server. Use an email client to download email. I'd also ask your new host to move the files for you they can probably do it a lot faster than you.
Yes, your new host can do it from server to server, which will be much more faster then downloading home, then reuploading.