  We calculated the magnetic dipole hyperfine interaction constants and the
electric field gradients of $2p^53p~^2[3/2]_2$ and $2p^53s~^2[3/2]^o_2$ levels
of Ne I by using the multiconfiguration Dirac-Hartree-Fock method. The
electronic factors contributing to the isotope shifts were also estimated for
the $\lambda = 614.5$ nm transition connecting these two states. Electron
correlation and relativistic effects including the Breit interaction were
investigated in details. Combining with recent measurements, we extracted the
nuclear quadrupole moment values for $^{20}$Ne and $^{23}$Ne with a smaller
uncertainty than the current available data. Isotope shifts in the
$2p^53p~^2[3/2]_2 - 2p^53s~^2[3/2]^o_2$ transition based on the present
calculated field- and mass-shift parameters are in good agreement with the
experimental values. However, the field shifts in this transition are two or
three orders of magnitude smaller than the mass shifts, making rather difficult
to deduce changes in nuclear charge mean square radii. According to our
theoretical predictions, we suggest to use instead transitions connecting
levels arising from the $2p^53s$ configuration to the ground state, for which
the normal mass shift and specific mass shift contributions counteract each
other, producing relatively small mass shifts that are only one order of
magnitude larger than relatively large field shifts, especially for the
$2p^53s~^2[1/2]^o_1 - 2p^6~^1S_0$ transition.
