Whether or not to go with LPI or Red Hat (or Novell/SUSE or whatever other Linux certification source) depends on whether you just want to be certified in a specific Linux distro or want to be certified for Linux in general. A Red Hat certification will target Red Hat (RHEL, CentOS, Fedora, perhaps Oracle Linux). An LPI certification will target a generic platform, giving you skills applicable to most modern distros.
If all you ever plan on working with is RHEL-based systems, then yeah, go with the Red Hat certs. Else, you should probably look into LPIC. Personally, I'd start with LPIC either way, since it's probably easier to go LPI->RH than RH->LPI (it's like building a house; it's nonsensical to build the roof before the walls and foundation).
At least that's the approach I'm taking; your own mileage may vary based on your own needs.