I'm occasionally asked by friends who would like to start a herb and veggie garden what plants to start with. The answer varies according to climate and soil type, so those would be the first things to establish. Are you in a cold climate, temperate, sub-tropical? This will greatly affect what you can grow well. The other thing to consider is soil type. This isn't an issue if you're going to use raised garden beds, which I'd recommend. The local soil type here is clay in which not much grows at all, although leeks like it.
Starting out in Winter will be frustrating because you're limited to what you can grow and it will grow slowly. But it is a great time to plan and prepare your vegetable garden. If buying raised garden beds I have found wooden frames (sleepers) as these have worked best for us. The stainless steel ones tend to heat up and dry out the soil. There are some concerns about wood treatments leeching into the soil but these concerns can be brought up against most types of garden bed containers so it's a matter of going with what you feel comfortable with. There is a big variety of garden bed edging that can be used - truck tyres, hay bales, bricks. What you choose depends on the look you are after and how temporary or permanent you want the bed to be. Stainless steel or sleepers are usually the preferred option because they are easy but if you hunt around, there are cheaper options - especially if you recycle. One of our beds was once a sandpit. I would recommend not skimping on soil though. Our local garden centre recently did an experiment by planting lettuces directly in a bag of their own soil and some in a bag of soil bought from the supermarket. The results spoke for themselves.
Consider the shape of the bed - you need to be able to easily reach the centre of the bed for sewing and harvesting. I love the idea of mandala gardens which are designed to avoid having to tread on soil - something I occasionally have to do to reach the back of one of our beds. This compacts the soil and makes it difficult for plants to grow so I am always careful to tread in the same spot. If you are fortunate enough to have the space, aim to have four garden beds - this allows for crop rotation. There's no such thing 'too much' of a harvest of something, you can make chutney or jam or other preserves and some vegetables (e.g. green beans, corn) freeze well. You can base the size of your garden bed according to your requirements but having more than one will help eliminate any soil problems. I find some plants work well in one bed but not in another according to shade, soil type, depth etc.
Most vegetable plants need full sunshine. Our best performing bed is one that gets full morning sun and dappled sun in the afternoon (shaded by the lemon tree). This is because it's not subject to the harsh early afternoon summer sun. Don't plant along a fence line - the bed won't get enough light - but if planting in the middle of the garden, consider that the bed may need some shade from midday sun in summer, depending on your location.
Radish are often said to be a good plant to sew first because they germinate quickly so you can see them appearing. Carrots take a long time to germinate and look like grass at first so while usually easy to grow, if you haven't planned your bed well, it can be easy to accidentally dig them up. Plant what you eat - there's no point planting radishes if nobody in the household eats them.
There are a couple of great apps and websites that can help you with deciding what to plant and when. One is Gardenate which gives monthly advice depending on your climate. I also like the Yates website for providing advice on what to sew and common problems. I've found that growing plants from seed is the easy part - keeping them alive is the real challenge!