I have an allotment and grow lots of veg. Currently I ve got growing, Peas for shoots and peas for pods, lettuce, spring onion, multi sown beetroot, cauliflower, broccoli, kohlrabi, pak choi, komatsuma aubergines/chillis (need to grow undercover in greenhouse not outside), spinach, chard, radish and spring cabbage. Usually these crops are all available to pick May/June. I haven t started my potatoes of yet as its bit early for me, I m in Lancashire and we re likely to get quite a bit of frost yet, but you could start of first early potatoes in tubs at home, just cover with fleece if there is any frost forecast and the leaves are coming through. If you want a quick crop first earlies are best, there is a variety called swift which I was harvesting last year at the end of May, its really fast, there are tastier potatoes but its not bad considering how fast it grows.
in April I ll be sowing, courgettes, Kale, kalattes carrots, parsnips, tomatoes, winter squash, leeks, outdoor cucumbers and sweetcorn. French beans grow really fast so I don't usually sow them until May and plant out in June.
If you want to grow any fruit, raspberries are my favourite, I grow autumn varieties as they are easy, will crop the same year you plant them and crop from August through to November.
Charles Dowding has a brilliant you tube channel all about veg growing, I learnt how to grow by watching his videos and reading his books. Huw Richards has a good book for anyone just beginning to grow veg as well called Veg in one bed. I love gardening, I find it so relaxing. Real seeds are my favourite place to buy seeds too.