Ställ era random astronomifrågor

No star collisions are expected from the Milky Way with Andromeda merger. Stars flying through each other's solar systems would be possible but exceedingly unlikely.

You are far more likely to have exciting sky stuff happening in a closed globular cluster.

If you still want to use the merger as a "historical setting" and in your story humans have not made it to the stars. You might make a series of solar system close approaches caused by the merger to make the human diaspora possible.

With computer simulation, the colonists could predict with some reasonable reliability the trajectory of the stars passing by (will get flung into intergalactic space, which will get flung into the core, and which will remain in the galaxy's habitable area - too close to the center and planets get cooked by supernovae - too far from the center and there's not enough heavier elements to sustain life.

One thing that will change is the collision of the two galaxies' gas and dust clouds. The collision will trigger massive and violent star forming areas. Some of these will form exceedingly large (e.g. 100M⊙100M⊙ - 100x the mass of the Sun). These stars burn hot, die quickly, and with a big bang (a Supernova).

A close approach of one of these to the Earth might spell the doom for every living thing on Earth.

There is a small chance that the Solar System will be flung out by tidal forces.
There is an equally small chance that the Solar System will be captured by Andromeda in the early stages of the collision, before the formation of the result of the merger.
Gas in the galaxies could be heated by an additional order of magnitude, from ~3××105 Kelvin to ~3××106 Kelvin. This alone could impact star-forming rates. Star formation is expected to increase anyway, due to other factors, although given that neither galaxy has a lot of gas, this will be minor compared with other collisions.
The result will most likely be an elliptical galaxy, leading to a different mass distribution and a slight change in the Solar System's orbit, even if most of the exotic tidal scenarios don't happen.