In this paper, we numerically investigate various hollow-core anti-resonant (HCAR) fibers towards low propagation and bend loss with effectively single-mode operation in the telecommunications window. We demonstrate how the propagation loss and higher-order mode modal contents are strongly influenced by the geometrical structure and the number of the anti-resonant cladding tubes. We found that 5-tube nested HC-AR fiber has a wider antiresonant band, lower loss, and larger higher-order mode extinction ratio than designs with 6 or more anti-resonant tubes. A loss ratio between the higher-order modes and fundamental mode, as high as 12,000, is obtained in a 5-tube nested HC-AR fiber. To the best of our knowledge, this is the largest higher-order mode extinction ratio demonstrated in a hollowcore fiber at 1.55 μm. In addition, we propose a modified 5-tube nested HC-AR fiber, with propagation loss below 1 dB/km from 1330 to 1660 nm. This fiber also has a small bend loss of ~15 dB/km for a bend radius of 1 cm.