SQL Server Log Shipping: File copy options?
If I roll my own log shipping, what are established ways to move the log file?


Why do you want to roll out your own logshipping solution ? Microsoft has put in a lot of effort for giving out-of-box Logshipping from SQL 2005 and up. This is tested by millions of customers since sql 2005, so highly unlikely you will encounter any bugs with it.

You can refer to : Step By Step SQL Server Log Shipping for how to configure native logshipping.  

References for Custom Logshipping :


Log shipping and A Control Mechanism
Custom Log Shipping
How to Setup Log Shipping for Multiple Databases


Using Powershell :


Log Shipping via PowerShell Invoke-LSRestore
Your poor man’s SQL Server log shipping-PowerShell version
Secure Log Shipping via SSL FTP
Automating SQL Log Shipping over SFTP (SSH), the simple way