It sounds like the cheapest way, off the shelf would be a Smart Relay, these are not expensive and can be had cheaper on ebay 220896492585.
You don't need any software to program it and it most likely has way more features than you may need.
They have internal timers and even set to a real time clock if you need that feature.
They are relabeled by a few manuf., Idec, Seimens, Square D, Omron etc.
They come in AC supply or L.V. supply models.