Data for red-shifting I am looking for basic data regarding red-shifting that  comes with reliable measure of distance of the emitting star.
Red shift is usually measured for galaxies rather than individual stars. Unless a star has just gone supernova, it's usually not bright enough to be seen even w the world's most powerful telescopes at the distances where cosmological redshift comes into play. Hubble's law operates over large distances; the expansion constant being 67.8 km/sec per megaparsec (3.3 million light years) 
Andomeda galaxy (M31) is 2.54 million light years away, and although some individual stars are visible at that distance, the galaxy has a net blueshift of 0.001001 (303 km/sec) due to its peculiar (i.e. non-Hubble) velocity.
Further out is where you start to see redshifts in excess of peculiar motion; and there you need to start using standard candles of some sort.
Cepheid variables when visible, Supernova, globular cluster brightness functions, are all used, as well as some spectral methods: Cosmic distance ladder

Supernova measurements go the furthest out, highest redshift, but are still a bit of a can of worms as far as interpretation goes.