It used to be easy, but these days...
As regards packing the kit, buy one of those bags with wheels on that has a decent shape, and then line it with pieces of hardboard to give the contents protection. Put your pit box contents into fishing tackle boxes, and your tyres into cardboard boxes, and seal each one with tape. Pack these things around the outside, and put chargers (in boxes) and other delicate stuff in the middle.
Now you've got the get on the 'plane!! You will have to take your kit as 'sports equipment' in order to get additional weight allowance. This will cost you about £15 per segment (£30 return). You will have to trawl through the Ryanair booking details for some time to find what you need!
Put the Tx and car into boxes and into your clothes luggage for maximum protection - watch the weight. You can try and take them through security as hand-luggage, but if Security don't like it, you've lost them. Some do, Some don't...
When doing fly-away races, I prefer to fly easyJet as Ryanair are a pain, although on the last trip to Germany, Ryanair were fine. Scheduled airlines are much less hassle providing you are in the weight limit, and you get a higher weight limit. And in case you think I am being too picky, take a look at this pic - yes that's my racing kit on top of that luggage trailer!!