I don't think it's practical to be self-sufficient unless you learn how to grow under cover. Cover provides you with a place to protect yourselves from the harsh weather (think greenhouse/polytunnel) and it also protects your veggies.
Let's step through the options, in a rough order of suitability, focusing on self-sufficiency. There's some overlap here with my general section on growing under cover, but read that too.
Lots of people successfully grow without cover and some even scoff at the need for it, but that's because they are mistaking vegetables surviving, with vegetables that are being actively harvested. Lots of plants will survive over winter, but a cover makes the difference between 20 harvests of spinach, and 5 harvests. If you want to eat rather than just grow, cover is your friend.
Not all covers are made equal, they vary in cost, longevity, effectiveness, flexibility, robustness and aesthetics. These dimensions also vary depending on the season.
For example one of my favourite solutions is a coldframe, with a simple polythene lid. It works great unless it's freezing cold and blowing a gale. When it's freezing, the lid often freezes to the frame, making it impossible to open. If you do open it - and there's a gale blowing - it's a deadly weapon! I was nearly knocked unconscious by a lid flying closed in a gust of wind and I've had several close calls! Fleece is brilliant in spring, but it gets ripped to shreds in winter and removing it when it's wet and frozen on a windy day is best not even thought about.
So lets step through the options and talk about them in the context of the 'challenges' of a self-sufficient life.
A polytunnel is by no means essential for self-sufficiency, provided you have some other forms of cover for your winter greens. It makes a big difference though and I don't think it's been an important part of my decision to continue with self-sufficiency. The main benefit is that it makes gardening a pleasure, no matter what the weather and provides much needed shelter when the weather turns. It's also a brilliant environment for bringing on seedlings.
I like planting a little of everything in the tunnel and then if it's blowing a gale, frozen, or raining I can always harvest something.
For more on polytunnels see this section of the book.
A greenhouse is more expensive than a polytunnel, so it tends to be smaller. It does have the advantage of being slightly warmer though. Normally warmer doesn't matter very much, because a layer of fleece in the polytunnel has a much bigger benefit than glass vs poly.
For more on greenhouses see this section of the book.
Low tunnels are great, they make a huge difference over winter and early spring. They work better than cold-frames. Mine are permanent structures though so they are hard to store when you don't need them in summer. In summer you have three options: disassemble them, store them, or use them. I use them, they work well for peppers, provided that are propped partly open, so they don't overheat.
I would always start with a cold-frame though, because it's 80% as good as a low tunnel, but easier to manage and to store away when not needed. I've a video that explains all the details: