Mangudai, definitely, they were pretty much elite skirmishers meant to draw the enemy out, siege equipment is easy enough since all of its the same, trebuchets, mangonels, battering rams etc, the mongols should rely mainly on mounted archers and light cavalry, they should have some heavy cavalry such as lancers and heavy cavalrymen with maces and spears, they should have a spearman and archer for their few foot troops but otherwise focus on all horsemen, they could have upgrades like composite bows, recurve bows, hardened leather armor and horse mastery. Oh and I remember reading that Tamerlane used war elephants after his indian conquests.