hey there ... there are four grips for a pullup/chinup ... underhand, overhand, mixed(one underhand, one overhand) and neutral grip(palms facing each other - the handles for neutral grip are found in most any gym). i guess there could be more types if you consider how far apart or close you grip the chinup bar ... (and if you are REALLY good, i suppose there are also one-handed pullups
To me, chinups are hard ... very hard ... requiring a strong grip, strong lats and back, and strong arms. You need to feel like you are pulling the bar to and through your chest. I think it is one of the best exercises to incorporate into one's workout.
I would say either neutral grip or underhand grip would make them easier ... they would engage your biceps more, along with your back.
I do the overhand grip, and only can get to 10, with my hands usually tiring out. then i grab the neutral grip handles and do 10, side-to-side(pulling myself to the right then the left), typically.
I will say, doing lat pulldowns one workout and chinups/pullups another might be a good strategy - the mix will make you stronger for each exercise. But remember, with each, stabilizing the core and really engaging the lats/back, is key. no excess body swinging or moving ... folks cheat all the time in lat pulldowns and chinups trying to create momentum, and renders the move less productive.
I hope this helps ... good luck.