This detailed and systematic theoretical study on the behavior of basic low dimensional (one- and two-dimensional) systems of early 3d transition metals should serve as a guideline to experimentalists as well as to theoreticians. We find that, lowering of dimensionality is favorable for emergence of magnetic ordering in all the systems studied, except Ti monolayers (MLs). For Ti MLs, both nonmagnetic and ferromagnetic states are degenerate within the numerical limits. For such a case, the interactions with substrate would play a decisive role in the magnetic ordering of the atoms in the ML. The total energy calculations show that the nonmagnetic and ferromagnetic states are almost degenerate for Cr and V MLs too; however, anti-ferromagnetic ordering is favored in these. The ferromagnetic ordering in Sc linear chains and anti-ferromagnetic ordering in MLs of Mn and Cr are found to be favored by a relatively larger margin showing good stability. Some low dimensional systems, showing electrons with only one kind of spin available at Fermi energy, may be suitable for spintronics related applications. The linear chains of Cr and Mn, and MLs of Sc are likely to form stable magnetic nanosystems as these exhibit almost saturated magnetic moment per atom around the equilibrium separation. The magnetic moment strengthens considerably as one goes from two- to one-dimension. Our results are supported qualitatively by available experimental results and offer a good insight into these nanosystems.