The CMS Inner Tracker, made of silicon pixel modules, will be entirely replaced for the operation at the High Luminosity LHC. One of the crucial components of the new Inner Tracker system is the readout chip, being developed by the RD53 Collaboration, and in particular its analogue front-end that receives the signal from the sensor and digitizes it. Three different analogue front-ends called Synchronous, Linear, and Differential were designed and implemented in the RD53A demonstrator chip. A dedicated evaluation program was carried out to select the most suitable design to build a radiation tolerant pixel detector able to sustain high particle rates with high efficiency and a small fraction of spurious pixel hits. The test results showed that all three analogue front-ends presented strong points, but also limitations. The Differential front-end demonstrated very low noise, but the threshold tuning became problematic after irradiation. Moreover, a saturation in the preamplifier feedback loop was limiting the signal return to baseline having an impact on the dead time. The Synchronous front-end showed very good timing performance, but also higher noise. The Linear front-end had all the studied performance parameters within requirements, but it had the largest time walk. This limitation was addressed and mitigated in an improved design. The analysis of the advantages and disadvantages of the three front-ends in the context of the CMS Inner Tracker operation requirements led to the selection of the Linear front-end for integration in the final CMS readout chip.