Electrons always jump from HOMO to LUMO. The ordering of MOs usually goes like this, in order of increasing energy: sigma bonding, pi bonding, pi anti-bonding, sigma anti-bonding. This is because sigma bonding orbitals are stabilized with respect to pi bonding orbitals because sigma bonding orbitals have end-on-end overlap. Therefore, since sigma anti-bonding orbital is de-stabilized as much as sigma bonding is stabilized, it's very high up in energy. On the other hand, pi bonding is less stabilized with respect to sigma bonding and therefore pi anti-bonding is less destabilized relative to sigma anti-bonding.
Just take a look of MO diagrams for various molecules. HOMO is generally a pi bonding orbital and LUMO is generally a pi anti-bonding orbital.