This paper presents a systematic analysis of inter-symbol and inter-carrier interference (ISCI) modeling in doubly dispersive channels for integrated sensing and communication (ISAC) systems. We propose a generalized OFDM (Weyl-Heisenberg) framework to evaluate four ISCI treatment approaches: (1) explicit estimation and compensation, (2) complete ignorance, (3) uncorrelated colored noise approximation, and (4) correlated colored noise modeling. Through continuous delay-Doppler channel characterization, we derive LMMSE channel estimators and corresponding estimation errors (as sensing metrics) for both pilot-assisted and fully-known symbol scenarios. The communication performance is quantified via ergodic capacity bounds under imperfect CSI. Our theoretical analysis and numerical results reveal fundamental performance-complexity trade-offs, providing insights for practical ISAC waveform and receiver design in doubly dispersive channels.