Gaussian parameters for IP and EA calculation
If you can afford to do so, it is always a good idea to compare calculations between at least two methods. Good results with B3LYP/6-31G(d) in particular are based upon favorable error cancellation, and B3LYP was not even parameterized against any data in particular (B3PW91 was parameterized for thermochemistry and the PW91 correlation functional was replaced with LYP without changing any other parameters). So, double-checking is wise!

Modern perturbation theory-based approaches have become much more affordable due to the density fitting (DF) and resolution of the identity (RI) approximations (same thing, different name), combined with spin-component scaling which may or may not improve things. The scaling is now roughly $O(N^4)$ and a small prefactor with basis set size; compare this with B3LYP at $O(N^3)$, exact MP2 at $O(N^5)$, CCSD at $O(N^6)$, and CCSD(T) at $O(N^7)$.

Energies are one of the most obvious improvements of range-separated or long-range-corrected (LRC) density functionals. Here the authors find that LC-$\omega$PBEh deviates little from $G_{0}W_{0}$, which is a workhorse for IE and EA calculations. Perhaps the most common new functional that is seeing quite a bit of use in the computational organic chemistry literature is M06-2X, which is shown here to perform even better than most approximate coupled cluster methods for this set of molecules (which are all closed shell!):



With regards to the basis set size, there is only one correct direction to go and that is up. You may be able to afford CCSD(T)/6-31G(d) calculations, but the results will be meaningless due to a severely deficient basis set for anything but the simplest calculations. See here for a recent discussion about the use of basis sets in DFT versus wavefunction methods. Wavefunction methods have always required larger basis sets for quantitative results, especially when not performing a basis set extrapolation. This would mean something like Dunning's correlation-consistent basis sets, augmented with diffuse and polarization functions, such as aug-cc-pVDZ or aug-cc-pVTZ if one can afford it. An interesting and effective truncation of these basis sets (they become very large) is given by Truhlar's "calendar" basis sets.

Less well-known are the requirements for LRC-DFT, which due to modern parameterization schemes are larger basis sets and larger integration grids for the XC contribution, often larger than what is default. Even Pople's triple-zeta sets based on 6-311G will offer some improvement, but the Ahlrichs def2 and Jensen's pcseg-n are probably better.

Finally, a word about the cost of LRC-DFT. Although its formal scaling cost is identical to traditional global hybrids such as B3LYP, in practice range-separated functionals may be 2-3x as expensive due to how the different contributions are calculated and then combined, depending upon the package being used.