I am planning to migrate my silverstripe site from one server to another. I found many related topic, but in my case I just wanted to Test my site on new server before completely Propagated. I followed further steps.
1. Backup database from old server.
2. Backup all file and folders.
3. Restore database on new server.
4. Upload files on new server.
5. Created new silverstripe-cache folder.
6. Edit _ss_environment e.g. Database name, username, password
I have tried couple of time with Silverstripe latest version (3.x) because my website already built in 3.x, hence I could not able to install it on my new host.
As you mention I will try to install older version and run it on temporary url, even I don't know it will work or not.
In that case I really suggest you either contact your hosting provider for a platform upgrade, or go for new hosting. Silverstripe 2.4 is no longer supported, so I'd advise against using it unless you already have an old site which you're not able to upgrad just yet...
My website migration completed successfully. I also run cms on temporary website url and it's work fine.
I only make changes in .htaccess BaseURL '/~username'. and flush database after all the upload (database and files ) done.