SQL Backups - Full vs Differential vs Log Shipping
By "log shipping" I'm guessing you're meaning log backup?  Log shipping is a high availability strategy.

If your full backups are taking the better part of a day, yes I recommend that you switch things up a bit.  But that all depends on a lot of environment specific parameters.  For instance, do you have a big window on the weekend where you will be able to do a full backup without interfering with users? (If not, you may need to look into filegroup backups)

A full backup once a week, and diff backups daily (again, in a maintenance window) is pretty common.  As for your t-log backups, you need to determine the maximum amount of allowable data loss.  In other words, if you back up your transaction logs every 30 minutes, you will have a maximum of 30 minutes data loss if the tail of the log is corrupt and unrecoverable.  So determination will need to be made for transaction log backups.

(P.S. If you actually did mean Log Shipping then please clarify and I'll rework this answer.  But by judging by your question I am assuming you just mean log backups)