The amount of angular momentum in a planet is incredible; planets are like giant gyroscopes.
The lowest tech level required would be "Dyson Sphere," because you'd need MASSIVE amounts of energy to attempt to add angular momentum to the planet.
Also note, due to conservation of angular momentum, you're going to need to "steal" momentum from an absolutely massive ... mass. We're talking, somehow transferring the angular momentum from Mars.
As for "fun side effects," let's say you have a Dyson Sphere, or a Dyson Ring to collect power. You use this to build an absolutely massive space ship; basically, it's engines surrounding a huge conglomeration of asteroids. Maybe you even turn Ceres into your vehicle. You fly Ceres to Mars, and use tractor beams on the north pole. This causes angular momentum to transfer to the ship, which you then whirl on to Venus, and use tractor beams on the south pole to re-transfer the momentum from the ship to Venus. Do this a couple trillion times and Mars will be tidally locked to the Sun, while Venus is spinning a bit faster.
Of course, once you've spent that much fuel, you might just put ion thrusters on ships, tractor beam them to the poles, and then fire rockets to rotate the ships (the angular momentum comes from the particles ejected into space).
This is a MASSIVE undertaking; we're talking about fantastic amounts of energy required. Equal, perhaps, to the energy required to initiate warp drive on a ship, to boldly go somewhere with habitable planets.
Or, eat a bit of crow and rehire the guy with the sunshield idea; it'll be way cheaper than a Dyson Ring, and makes a great place to put orbital solar power stations.