are you using the data exporter or transferring the files and database from one host to another?
php.ini some hosts allow some changes to be made and you place a php.ini in root folder of the site you are wanting to make changes to.
Upload the zip into a folder created by you within your host then use the extract function within filemanager in cpanel. This is quicker than ftp as ftp does a few files at a time. You are uploading them all using cpanel.