The terrestrial version are called Tetrapods (literally "four feet"), which originated about 350 million years ago, with modern descendants being amphibians, reptiles, birds, and mammals (though some have subsequently lost tails like us, or feet like snakes).

However, these limbs are just modifications of pectoral and pelvic fins of our fishy ancestors. The true origin of this body plan is 435 million years ago, with gnathostomes, the jawed vertebrates. This is the origin of the two pairs of fins, which eventually became limbs.

For vertebrae it started with fish. Four fins, head and tail.

A good book about the line of fish to vertebrate is Your Inner Fish by Shubin

For insects it started earlier.

It probably originated simply from practical reasons... You want your head at the front to sense where you're going, and you want waste behind you so you don't run into it/eat it again. The limbs on the sides therefore is the best spots (of course there are exceptions to this body plan... Sponges, jellyfish, etc)

These are called tetrapods, descendants of the lobe finned fish. We all share this body plan because afawk fish only made the change to fully terrestrial life once, and all living exclusive lung breathers are descendants of the species that did. Fun fact, this means that technically, whales actually are fish after all.

Already great answers here, but I'll go back even further. OP might be referring to when things started with bilateral symmetry as a body plan. Right about 600 million years ago right before the Cambrian period. Before that, most everything was radial symmetry. Think sea anemone. Once bilateral started you started getting two eyes and all sorts of fun stuff. We go back a loooong way !

Major appreciation to everyone who commented, that gives me great starting points to read more. I was watching a science education channel on ytube recently that pointed out how many creatures are sort of morphs of the same basic internal bome structure and it was really wild to internalize that.