If you are finding it uncomfortable on your neck, the bar is probably sitting too high.

The bar should be sitting on your upper back area – your traps.

To find the right position, try bringing your head down and feel around the back of your neck. You should feel a couple of bones around the back-bottom of your neck, meeting your upper back. Sit the bar about an inch lower than these bones.

The bar should feel as if it is sitting on a shelf.

I’d recommend the book Starting Strength to anyone looking to learn how to lift properly

certainly the squat involves more muscles than the leg press aside from the quads, glutes and hams. free weights pose more challenge to more muscle groups than machines. since you have to balance a barbell on your shoulders, it would engage stabilizing muscles in the process. your biceps, delts, traps, back and core will also be somehow involved. in fact, the squat is one of those exercises recommended for total body workout:)

actually, most people find squatting uncomfortable but once you get used to it, you will discover it has greater effects like improving posture. just make sure you execute it correctly.

if it hurts, make sure you have a foam or cushion around the area of the bar on your neck. or change a bit where you place the bar. make sure your neck is not strained by the weight by letting your traps have a share of the weight. or maybe you use too much pounds/kgs so decrease the weight and focus on right execution.

or, if you are still getting acquainted with the squat, do it with a smith machine for the meantime that you find it awkward.

there is nothing wrong if you use the leg press because it is safer since it is machine-assisted but it is better if you vary the exercises you do to make the most of your workout. perhaps on some leg days you do squats then on others, leg presses.

Good Luck