We have traveled many times with our 3 year old starting when she was two months old. We travel less now that we have two kids but, I feel I like we've got a good system down.
Bring the car seat even if there is the slightest chance of there being an extra seat, they can always gate check it if they have to. This is especially helpful if he can sleep in his car seat. We bring a stroller to navigate the airport. This will also have to be gate checked. I prefer to bring my larger stroller as opposed to a little umbrella one so I can utilize the basket underneath and balance the car seat across the top. With the child in the stroller, I could tow a rolling suitcase and not have to check anything on short trips. If you are planning on checking luggage, then you may be able to get away with the smaller stroller. Just remember that a car seat can be a pain to carry around, not heavy just awkward, although not so bad if there are two of you.
I always prefer renting cars because I think it is fun to get around on our own. However, it depends on how comfortable you are driving in unfamiliar places. But, it is easier than hauling your car seat in and out of taxis. Depending on your comfort level, many places wouldn't require that you have a car seat in a taxi, many don't even have seat belts.
I've never had to use benadryl, even on a 17 hour car trip with both kids. But, I still bring it. Make sure to talk to your doctor about proper dosage and you'll want to give it a trial run. It can have the opposite effect on some children, making them wired.
I nursed my kids during take off and landing to help with their ears. Later my daughter used a bottle for this until she was almost three. In light of recent events, I'm not sure how the rules will be about bringing liquids on planes. But, if you plan to use a bottle try to bring plenty of milk or whatever you put in his bottle. Sometimes they cannot get anything from the beverage service carts until after take-off. It can be problematic if you are stuck on a runway and the milk runs out.
We bring a lap top that can play DVD's, make sure your battery will last through the whole movie or bring a back-up battery. My husband usually has to bring it for work anyway. Also, bring earphones so the other passengers don't have to listen.
If he likes drawing, magnadoodles are much easier that picking up pencils and crayons over and over.
We got our daughter a small Hello Kitty rolling suitcase and she fills it with small books and other toys. It was also extremely cute to watch her toddle around with it in the airport and at the gate while waiting to board. It also made her feel like a big girl and made travel more fun.
I try not to bring toys that make noise. But, if he has a favorite you can always put duct tape or packing tape over the speaker to help muffle the sound.
I find the best way to keep them occupied is to give them one book or toy at a time, rotate them so they seem fresh. Once in the air walk up and down the aisle when he gets squirmy.
Bring snacks for the plane.
Keep in mind that the tray table may not unfold properly if he is in his car seat (he'll be too high up). This can make mealtime interesting.
I also bring a box of their favorite crackers in my checked luggage for the rest of the trip and the return flight. Even though they are adventurous eaters, it is nice to have something familiar to eat. Even if it is only at snack time.
I never tried to train my kids for the time difference. But, we've never been as far a Europe with them. I just try to schedule things around their sleep needs. Most times they catch up on sleep during car rides, if you'll be getting around that way. They also can catch up on sleep in the stroller if you're out sight seeing.
I hope that some of this info was helpful. I'd happily try to answer any other questions about travel as well.
Good luck and have fun!
T.