Combinatorially synthesized materials, especially cationic polymers (CPs), with gene transfection function hold great promise in nanotechnology. However, the main limitations of the existing CPs [such as polyethylenimine (PEI), poly-l-arginine, or polyamidoamine-based dendrimers] as gene transfection agents are high cytotoxicity in the physiological environment. We have developed novel CPs composed of polyamines—endogeneous tetraamine spermine (Spm) and synthetically made triamine N-(2-aminoethyl)-1,3-propanediamine (Apd) for incorporating sec-amino groups and imparting PEI-like structure to the CP backbones. Naturally occurring building blocks such as amino acid arginine (R) was also used for incorporating guanidine-groups into the CPs. The cytotoxicity of resulting CPs—polyureas (PUs) and polyamides such as polysuccinamides and R-attached polymalamides was evaluated using murine and human fibroblasts and carcinoma cell lines. The cell compatibility screening revealed that the CPs made of Apd are less cytotoxic compared to Spm-based analogues. From the novel polymer library, total of six polymers were further studied for oligonucleotide (pDNA) complexation and transfection abilities. Highly water-soluble CPs formed nano-sized polyplexes with pDNA at rather low CP/pDNA weight ratios and showed less cytotoxicity and higher transfection ability compared to widely used PEI as well as commercially available transfection agents. Furthermore, new CPs showed selective transfection activity toward certain cell lines (4T1, HeLa, NIH3T3, and CCD 27SK), which is important for their potential applications in gene therapy.