Shkadov Thrusters

Shkadov Thruster and Dyson Rings (via Wikipedia)

A Shkadov Thruster is a proposed sort of stellar engine, which would be used to move an entire star system by redirecting the primary's radiation pressure. A star being piloted by a Shkadov Thruster wouldn't move very fast (if we built one for Sol, after 1 million years we would have moved less than .1 parsec), but given enough time it could end up moving fast relative to the surrounding stars.

Of course, the Sun is probably bigger than need be. A particularly luminous but much less massive star could accelerate much faster. Alternatively, a somewhat more massive but much more luminous star (F3, for example) might accelerate faster (I haven't done the math on it).

Additionally, energy collected by a Class C engine could supplement the thruster's thrust. Suppose a ring of collectors was set up about the star's equator, and the thruster was located above one the poles. The energy that might have headed out from the equator could instead by directed to electric propulsion drives.

What sort of star to use for this would depend in large part on how fast and far the architects want to go, and how long they want to be able to see returns on their investment.