Cut chicken wings at joints and discard chicken wing tips (or reserve to make stock). Rinse remaining wing pieces and pat dry. Arrange in a single layer on a greased 13x18-in. jelly roll pan. Bake until golden brown, about 30 minutes.
Meanwhile, prepare red hot sauce. Remove pan from oven, drain off and discard fat. Pour hot sauce over chicken; turning wings to coat well. Continue baking, uncovered, turning wings once or twice, for about 15 minutes or until sauce is bubbly and edges of wings are crisp.
Meanwhile, prepare blue cheese dip in a small serving bowl.
For the red hot sauce:
In a small bowl, stir together white vinegar, water, tomato paste, sugar, liquid hot pepper seasoning and 1 to 3 tsp. cayenne pepper.
For the blue cheese dip:
In a bowl, coarsely mash cheese and stir in sour cream, garlic, dry mustard and pepper. If made ahead, cover and refrigerate for up to 3 days. Makes about 1-1/3 c.
Arrange chicken on a platter and serve celery sticks and blue cheese dip.