In some cases, "echarse a" and "echar a" are actually the same expression, the "se" can optionally be added as a reinforcement. El hombre echó a correr = El hombre se echó a correr. In other cases, you need the "se". The following expressions, for example, require the particle me, te, se, etc. Mi madre se echó a llorar. Tengo que echarme a dormir. La comida se echó a perder. "Echar a" meaning to begin something is not super useful as an expression, but in some cases you need it. El pájaro echó a volar. You could say "empezó a volar" pero it doesn't sound natural. In any case, depending on your level, it's enough to have a passive understanding of their meaning as there are several other ways of communicating the same idea.

Hola Richard, El uso de "echar a" como significado de "empezar" está muy limitado, te pongo un par de ejemplos: Yo eché a andar a los 2 años = Yo empecé a andar a los 2 años. La empresa echará a rodar el mes que viene = La empresa empezará a funcionar el mes que viene. Un saludo