Hi,
Grow dwarf green beans! They are upright and very, very easy to grow, they crop like crazy and it's a lot of fun lifting the leaves and finding yet another crop of perfect beans. I have never gone wrong with them. The dwarf variety is easiest if you only have pots or a small patch. Start then off in March indoors and just follow the instructions on the packet to plant them out after the risk of frost has gone, which is usually around April.
Herbs are also good fun to grow and look nice in little pots - coriander, chives, basil, parsley are all easy to grow assuming you manage to germinate the seeds successfully!
Another really easy thing to grow is radishes, you sow direct into a well-dug patch and then just wait. If you just sow a small number of seeds every few days, then you won't end up with them all cropping ripe at the exact same time.
Last year I had a lot of success growing rocket, but it likes cooler weather and tends to run away to seed if you don't keep it cool and keep eating the leaves. I saved an absolute fortune in overpriced salad bags, and once it ran to seed I collected the seeds and hope to try again this year!
Chillies you need to start right away indoors, they need a LOT of warmth and sun to get a good crop. My mum always had them on a sunny windowsill and they did great, but I've never had a good crop of them outside.
Courgettes are fantastic. You might only want a handful of plants as the plants grow really big - I usually pick three good seedlings and give the other seedlings away. They need PLENTY of space, as they have huge leaves and you dont want them overlapping as they can get this silvery mildew on the leaves that causes problems (always water the plants at the base, never water the leaves).
Cherry Toms are ideal for a beginner. When you've got the seedlings going, you want to get your tomatoes planted out after any risk of frost is over, in the sunniest position possible, up against a sunny wall is fab if you can manage it. Last year, i started lots of plants, kept some inside for longer and put some out quite early, my best plants were ones i kept indoors for longer. They don't appreciate cold nights or cold wind.