Lots of advice to be given, but start with Carol Klein's veg book. She's fab
Consider putting in raised beds, it makes growing so much easier. You can but kits or just use boards or sleepers. Makes it easier to contril depth. And snails.
Agree about carrots, waste of time and tricky
Grow things that are unusual varieties, expensive or you love. Carrots take up a lot of space for three quid's worth of produce.
Salad is so worth it. You will never buy a crappy salad bag again. Look at Suttons for varieties, especially the spicy ones. Same for spinach.
Courgettes are really easy and the results are impressive.
Hanging basket tomatoes are good, depending on where in the UK you are. If in S England, great, if N Scotland, don't do it without a greenhouse, but you need to be sowing indoors now. Or cheat and but small plants in a few months.
Peas are great too, especially if you have young kids. As are strawberries, but again, they take up a lots of space for not a lots of yield.
Good luck