Which groups were intended to benefit the most from the Great Society?

Poor people and minorities.

Another take...The intended beneficiaries of LBJ's "Great Society" were -- and still are -- the Democrats.

All rosy rhetoric aside, Johnson's grand plan was meant to benefit his own party and himself. It was carefully crafted to carve specific blocks of votes away from the crowd. Blacks, women, elderly, and children (the kind approaching voting age), other minorities. The usual assortment of unhappy groups. (Or groups that could be made unhappy.)

These separate groups were combined to form a Democrat powerhouse that put LBJ in office in 1964 and fueled the "socially responsible" legislation of 1965-1966 -- the "Great Society" crap -- through Congress.
It was intended for minorities and poor people to benefit most from the Great Society.