Using old robot vacuum cleaner base
As my interest was more the AI of a robot than building the base itself so I figured using a basic robot vacuum cleaner as a robot base would be a good cheap start. You would still need to understand how to make use of (program) any of its sensors or any you may add.
A similar project is started here. The author's last post was 20th March 2019 so I assume he ran out of steam. Still it gives some idea of how to go about it.
There may be other projects of interest there as well.