Pulsar timing arrays (PTAs) are Galactic-scale nanohertz-frequency gravitational wave (GW) detectors. Recently, several PTAs have found evidence for the presence of GWs in their datasets, but none of them have achieved a community-defined definitive (> 5σ) detection. Here, we identify limiting noise sources for PTAs and quantify their impact on sensitivity to GWs under different observing and noise modelling strategies. First, we search for intrinsic pulse jitter in a sample of 89 millisecond pulsars (MSPs) observed by the MeerKAT Pulsar Timing Array and obtain new jitter measurements for 20 MSPs. We then forecast jitter noise in pulsars for the future SKA-Mid telescope, finding that the timing precision of many of the best-timed MSPs would be dominated by jitter noise. We then consider dispersion measure variations from the interstellar medium and find that their effects are best mitigated by modelling them as a stationary Gaussian process with a power-law spectrum. Improving upon the established hasasia code for PTA sensitivity analysis, we assess the timing potential of the lower frequency UHF-band (544–1088 MHz) of MeerKAT and find a potential increase in GW background sensitivity by ≈ 8%, relative to observing at L-band. We show that this improvement relies on assumptions on the propagation through the interstellar medium, and highlight that if observing frequency-dependent propagation effects, such as scattering noise, are present, where noise is not completely correlated across observing frequency, then the improvement is significantly diminished. Using the multi-frequency receivers and sub-arraying flexibility of MeerKAT, we find that focussed, high-cadence observations of the best MSPs can enhance the sensitivity of the array for both the continuous GWs and stochastic GW background. These results highlight the role of MeerKAT and the MPTA in the context of international GW search efforts.