I'm not sure which bulbs would do best in clay soil, but I would choose a variety of the cheaper and hardier ones and have fun.
I am fond of tulips, common crocus and daffodils because they come in a wide variety of colors and are easy to find. If you have rodent problems, tulips seem to be squirrel and rabbit magnets but nothing eats daffodils (they are poisonous). Bulbs can be planted in the middle of everything else, if you dig one up by accident in the summer, just plant it back. If you take it slow and add a little more each year, you have a chance to figure out which make you happiest in terms of color, season and survival rate.