In this paper we study bright M{type giants found in the First Byurakan Survey (FBS) low-resolution (lr) spectroscopic data base. Phase dependence light-curves from large sky area variability data bases such as Catalina Sky Survey (CSS) and All-Sky Automated Survey for Supernovae (ASAS-SN), and the second Gaia data release data (Gaia DR2) high-quality photometric data are analyzed to estimate some important physical parameters for 1096 M-type giants found at high Galactic latitudes. Their Gaia DR2 broad-band G magnitudes are in the range 8.0 < G < 16.0 mag. Gaia DR2 radial velocities (RV) are available for 134 and luminosities for 158 stars out of 1096. The Gaia DR2 color/absolute magnitude diagram (CaMD), their Galactic distribution, also some other diagrams based on Gaia DR2 photometric data are presented. Absolute magnitudes cover the range +1.0 > M(G) > -5.4 mag. They follow to the behaviors and occupy the same regions on the color-magnitude diagrams studied in many papers by different researches for long period variables (LPVs). Particularly, we consider the locations of the FBS giants on the new diagrams, using multi-band approaches in combination with Wesenheit functions, obtained recently by Lebzelter and colleagues (2018) for the oxygen-rich (O-rich) and carbon-rich (C-rich) LPVs in the Large Magellanic Cloud. Period-Luminosity (P-L) diagram was presented for 112 M Mira-variables. The upper limit of the initial stellar masses can be estimate near 5 Msun for M giants according to the new diagnostic tools. The kinematic properties, space distribution also more interesting cases among the sample were considered.