People - kids included make noise on the plane. The worst behaviour I've seen has been from adults - a child being upset for takeoff is so completely understandable and wouldn't bat an eyelid amongst anyone but the most grumpy of people.
So my top tips (and people don't even realise I have kids with me half the time - although mine are both NT) - ipads/phone and headphones loaded up with TV (netflix and iplayer both let you download now). Try and keep to one carry on which is small enough to go under the seat in front, with sweets, aforementioned ipads, drinks (bought past security, in case you need it before the trolley comes down - plus they're cheaper), battery packs (if long flight).
When take off comes, try and act excited - I generally have to stop my kids yelling in excitement rather than fear these days. In fact, I've taken to plugging them into the devices as soon as they are in their seats so they don't even notice takeoff.
Don't take activity boxes/crayons etc. They will be dropped, and you will spend half the flight rummaging on the floor and asking those around you to do the same.
For the little one, there's actually a surprising amount of room on the floor between your legs - especially if your other child sits cross legged. It's a bit dirty, but if all else fails, it's better than a squirming upset child on your lap for hours - hopefully you'll get someone fairly easy going in the third seat/they'll manage to sit you in a row with an empty seat.
Good luck - I fly alone with my two fairly frequently, and generally it's fine.