If I have a unit on a battlefield that states "At the start of your beginning phase, Draw 1," and a unit with the ability that states "When I hold Draw 1," what is the sequence the abilities resolve at the start of turn in relation to gaining a point?

The "start of Beginning Phase" draw resolves first — before you gain the point. The "when I hold" draw resolves after the point is gained.

Sequence: the Beginning Phase's Beginning Step ("at the start of Beginning Phase" effects, Rule 315.2.a) comes before its Scoring Step, where you Hold and score the point (Rule 315.2.b). So your start-of-phase draw fully resolves, then you gain the Hold point, then the "when I hold" trigger is placed on the Chain and resolves (Rule 383.4.d, FAQ #7628).

Also note: if both draw triggers came from the same event they'd be ordered by their controllers — but these aren't simultaneous, so the fixed step order applies regardless of card choice.