I can give you some reactions, that should differ with different concentrations and temperatures. There's the classic reaction of Baking Soda with Vinegar. It should be noted that the concentration of Acetic Acid in Vinegar is only 0.3%. Would a stronger concentration of acid accelerate this already vigorous reaction?
Another is decomposition of Hydrogen Peroxide with the catalyst Manganese Dioxide. It's an exothermic reaction, so would heating or cooling this reaction change its rate?
You could do the displacement of Copper in Copper (II) Chloride by Aluminum. Different molarities of the Copper (II) Chloride solution will produce different rates of reaction (I've observed it), and other factors may influence its production. Make sure you use Copper Chloride, not Copper Nitrate (that displacement doesn't produce a gas).
You could dissolve copper in Nitric Acid, but make sure you have a Chemistry hood if you do it, as it will produce a lot of poisonous gas. I would think that the concentration of the Nitric Acid would affect the rate of reaction. I wouldn't be surprised if temperatures played a role.
One other one, that might be a little dangerous, but would definitely have plenty of opportunity to adjust rate of reaction: decomposing Salt with electricity. Varying the voltage, the amperage, the temperature of the salt, and the type of salt (iodized, plain, sea etc.) could change the rate of reaction and the products of the reaction. However, with the fact that the gas produced is Chlorine, you might need special permission.