I am a lymphedema therapist, and recommend compression stockings to each of my patients. We typically recommend the brand Juzo or (less frequently) Jobst stockings. I would go with a compression level of at least 20-30 mmHg (also called Compression Class I), especially for flying. That's a good starting point for consistent swelling, but you can always increase the level of compression if needed- some people need 30-40 mmHg or higher. You should be fine with a knee-high stocking, and you can choose open or closed toe depending on your preference and which stocking you choose. A prescription will be needed if you want to submit it to insurance through a medical supply store. If you order online, or pay in full without insurance, a prescription is not needed. We usually refer people to an online company called lymphedema products, though there are many others. You can get stockings at Walmart, etc, but they are not manufactured the same way and are therefore cheaper (cheaper is not better in this case)! It's worth the investment to get a quality product that will last longer, work better, and be more comfortable.
Good luck!
ETA: The company I mentioned above provides a sizing chart on their website; you will need to use a tape measure for several points on your leg. You can probably figure out the correct size on your own. Alternatively, you can get measured at a medical supply store.
Also, if you have chronic swelling that does not ever totally go away, you need to be referred to a Certified Lymphedema Therapist for therapy. Compression stockings alone do not reduce swelling, but instead prevent further swelling- if the correct amount of compression is applied and if they are worn appropriately.
