There's a great guide on how to fly with motorcycle gear psoted on Ride Apart, which goes through all the questions you asked point by point. Starting with the type of luggage, it suggests a duffel bag, small enough to be considered a carry-on, and large enough to fit all your gear. You don't have to buy this exact bag, but you might want to find a similar configuration.
Regarding the helmet, you can carry it on a plane as your personal hand-luggage item. Place it in a padded helmet bag, haul it over your shoulder and you're good to go. As an added precaution, make sure that your ticket fare allows you one personal hand-luggage item (European low-cost carriers sometimes don't so check this). Quoting from the linked site:
So how do you get it on a plane? You carry it with you as your personal item. Just throw it in a helmet bag (Bell makes the best ones, they come with any new helmet purchase) and tell anyone who asks that it’s your murse. Airport security apparently isn’t aware that these things make excellent blunt impact weapons; I’ve only been hassled once, in Heathrow, immediately following a terrorist attack in that country. It’s never once raised an eyebrow elsewhere and even makes a great conversation starter if you happen to sit next to a pretty girl...or guy. Just keep in mind that it likely won’t fit under your seat and needs to go in the overhead.
The rest of the gear can safely go in the duffel bag. The leather suit, armour, boots, and gloves are unlikely to be considered as dangerous/prohibited items. The only issue you might have is if your gear contains metal padding/plates. These are becoming more and more common on both gloves and leathers, and might raise an eyebrow or two.
A final tip: if you have a two-piece leather suit, wear the jacket on the flight, and pack the bottoms in the bag. Just remember to remove your back protector since it'll be uncomfortable during the flight.
