My lawn is in a poor state partially caused by the ground collecting
water in the winter which kills off a big patch of grass. Also the
grass seems poor quality and is thin with many weeds (and different
types of grass).

I want to rotovate the lawn to try and get it level but would
appreciate some advice on how to do it best.

Things I was thinking off we

Maybe kill off the original grass first by covering it

Add sand to the soil and mix it in for better drainage.

Mix the seeds into the top layer of soil rather than putting them on
top.

Will a rotovator chop the soil small enough?

Does the soil need rolling flat after doing this?

Maybe check the soil PH?