Most lifters are extremely quad-dominant, and leg curls are underrated as a hamstring developer. Starting your workout with leg curls allows you to place considerable emphasis on the hamstrings, as opposed to just tossing in a few meaningless sets at the end of your leg workout.
With pumped hams, you'll feel sturdier in the bottom position of the squat and your hips will seem greased during each squat rep. And as strange as it sounds, you'll find that your knees need less warming up after starting with leg curls.
Do 2-3 warm-up sets for the hamstring curls, then 3 sets of 8 reps with a hard flex at the top. On the fourth set, do 8 reps followed by 25 partials from the stretched position – just move the weight 4-6 inches from the bottom. Then squat and see how it feels.