Humility and +1/+1 counters
Your vampire will be larger than 1/1.
The relevant rules reference is the power/toughness layer when handling continuous effects. Note that because of this layering rule, it doesn't matter whether the creature entered the battlefield first, or the Humility.

613.3. Within layer 7, apply effects in a series of sublayers in the order described below. Within each sublayer, apply effects in timestamp order. (See rule 613.6.) Note that dependency may alter the order in which effects are applied within a sublayer. (See rule 613.7.)
613.3a Layer 7a: Effects from characteristic-defining abilities that define power and/or toughness are applied. See rule 604.3.
613.3b Layer 7b: Effects that set power and/or toughness to a specific number or value are applied. (That is the Humility)
613.3c Layer 7c: Effects that modify power and/or toughness (but don’t set power and/or toughness to a specific number or value) are applied.
613.3d Layer 7d: Power and/or toughness changes from counters are applied. See rule 121, “Counters.” (the +1/+1 counters)
613.3e Layer 7e: Effects that switch a creature’s power and toughness are applied. Such effects take the value of power and apply it to the creature’s toughness, and take the value of toughness and apply it to the creature’s power.
Example: A 1/3 creature is given +0/+1 by an effect. Then another effect switches the creature’s power and toughness. Its new power and toughness is 4/1. A new effect gives the creature +5/+0. Its “unswitched” power and toughness would be 6/4, so its actual power and toughness is 4/6.
Example: A 1/3 creature is given +0/+1 by an effect. Then another effect switches the creature’s power and toughness. Its new power and toughness is 4/1. If the +0/+1 effect ends before the switch effect ends, the creature becomes 3/1.