If you can afford it, business class is the best answer for extra space. In general, I feel that first class isn't worth the premium. There are three basic ways you can get one of these seats. You can buy business class seats, paying full fare ($$$). You can use miles to upgrade or to pay for your entire ticket with miles. There are also brokers who can get you discounted business class seats. I understand that the discounts can be substantial. You can find them with a search on the web, or perhaps someone on this forum has used one of them.
For international travel, I almost always buy a qualifying coach seat and upgrade with miles. It normally costs a bit more than the lowest priced economy seat. It isn't always easy, and can require some patience, but it works for me. It is so much more comfortable than coach. You have a good chance of getting some sleep on the seats that turn into a lay-flat bed. On a 12 - 14 hour flight, you can actually get a full night's rest. A lot of how well you sleep will depend on your own sleep habits. I am used to it and am able to sleep as well in business class on an international flight, as I can in many hotel rooms. In my opinion, it is money (or miles) well spent.