Classical novae are the result of thermonuclear flashes of hydrogen accreted by CO or ONe white dwarfs, leading eventually to the dynamic ejection of the surface layers. These are observationally known to be enriched in heavy elements, such as C, O and Ne, that must originate in layers below the H-flash convection zone. Building on our previous work, we now present stellar evolution simulations of ONe novae and provide a comprehensive comparison of our models with published ones. Some of our models include exponential convective boundary mixing to account for the observed enrichment of the nova ejecta even when accreted material has a solar abundance distribution. Our models produce maximum temperature evolution profiles and nucleosynthesis yields in good agreement with models that generate enriched ejecta by assuming that the accreted material was pre-mixed. We confirm for ONe novae the result we reported previously, i.e. we found that 3He could be produced in situ in solar-composition envelopes accreted with slow rates (Ṁ<10-10 M⊙ yr-1) by cold (TWD < 107 K) CO WDs, and that convection was triggered by 3He burning before the nova outburst in that case. In addition, we now find that the interplay between the 3He production and destruction in the solar-composition envelope accreted with an intermediate rate, e.g. Ṁ=10-10M⊙ yr-1, by the 1.15 M⊙ ONe WD with a relatively high initial central temperature, e.g. TWD = 15 × 106 K, leads to the formation of a thick radiative buffer zone that separates the bottom of the convective envelope from the WD surface. We present detailed nucleosynthesis calculations based on the post-processing technique, and demonstrate in which way much simpler single-zone T and ρ trajectories extracted from the multi-zone stellar evolution simulations can be used, in lieu of full multi-zone simulations, to analyse the sensitivity of nova abundance predictions on nuclear reaction rate uncertainties. Trajectories for both CO and ONe nova models for different central temperatures and accretion rates are provided. We compare our nova simulations with observations of novae and pre-solar grains believed to originate in novae.