You really need to think about what you're solving here. If it's DR, then you can't worry about reading data from the secondary. If it's scale out, that's separate.
In either mirroring or log shipping, if a large transaction comes through, it needs to move to the secondary site. If you don't move it because it's too large in Log Shipping (LS), then what will you do? Move another backup instead and reset things? You have to move it somehow.
One thing with LS, you can set up two separate restores from the same files being copied. So you could have a DR one that restores every 15 minutes, and another that is readable and restores on a different schedule (maybe all logs every 4 hours). That would give you a decent window to continue to read data from the secondary.
If you search Log Shipping or Mirroring, there are some articles on this site as well that might help you get started.
http://www.sqlservercentral.com/articles/104391/
http://www.sqlservercentral.com/articles/62676/