Marigolds or an herb of some sort come to my mind. It's the end of summer here and without knowing your zone there isn't much that would grow fast enough.

Basil is very quick and easy to grow, but ditto on the possible "winter's coming" problem.

If you're growing indoors and have reasonable light you could try french beans, peas, or the cress you can cut for use in sandwiches.

You could also try wheat berries, alfalfa, radishes or any of the vegie seeds used for growing sprouts.

zinnias, differs by variety so read the package, small flowered ones will bloom quicker than the tall big flowered ones (but they require full sun). The old stand by is radishes are fast growers too.

Be aware that most plants need sun only after they germinate. So germination rate would be a poor experiment if your showing the difference between sun and not sun, instead you would need growth rate.

I don't think we have enough information to help you out, right now. Are you going to provide special high foot candle lighting? If not, the flowering plants and vegetables just won't do. If you are, then you have a great many options regarding the indoor part. However, we don't know what part of the country you are in, thus can't recommend an outdoor plant at all.

Are you looking for something that would be expected to flower.....and are you going to be manipulating the day length?

Do you need to produce something from seed and observe it throughout the development?

Give us more information and perhaps we can make some suggestions. Sounds like this is a science fair project.

if the duration of the experiment is less than 1 month, your best choices are peas (remember to include some sort of support for them), leaf lettuces, and 'cat grass' or wheat grass. they all have easily measurable growth patterns, can be grown in small spaces, and give a uniform look to such a project.