Spring onions and salad leaves are pretty easy for most people to grow, and useful for most houses. Get the "cut and come again" type salad mixes, as you can pull a few outer leaves from the plants and the inside leaves will keep growing, meaning you can have salad for months on end. Spinach, to do the same (picking outer leave) as baby leaves, is also good.
Tomatoes, especially if you get plants rather than seed, are also good for beginners and tend to give a good crop.
Peas are also good, and think about ones with edible pods like Mange tout or sugar snaps.
Beans - I think broad beans are easiest for beginners - they just grow up from the soil and can support themselves. Dwarf French beans (dwarf meaning they don't grow very tall so don't need supporting on bamboo canes) are also good, for soil or for window-box type pots. And you can now get other kinds of beans in dwarf form, like borlotti beans, which are lovely and colourful as well as being good to eat the internal bean. And possibly runner beans - runner beans and French beans are the only ones that you eat the "pod", the rest need to mature enough to eat the bean inside and not the pod. But even french and runner ones, if you let them grow "too long", you can peel off the pod and just eat the beans inside. (And the same thing for the peas that you eat the pod - if you let them grow too big and the pods aren't nice anymore, just pod them as if they were ordinary peas and just eat the round peas from inside).
For beginners, "dwarf" types of peas and beans are useful as they don't need much support because they don't grow that tall - maybe 1-2 feet. Whereas other types can grow between 4 and 6-8 feet and need canes or netting to support the plants.
Radishes are quick to grow - sow a few (maybe a row about a foot long) every week or so, and you will have them all summer long.
Have a look at companies such as Suttons Seeds and THompson and Morgan, in their children's seeds sections, to see what they think are easy and fun to grow. They tend to be good pointers for beginners.