What would be a fair day rate for a 1-day excavation job involving 1 person and a 24" bucket excavator?
Price is going to depend on many factors that vary by location.
Call several different local contractors, pick the one you like best.
Get the biggest machine you can fit on the site, eg: a 4 foot bucket holds 8 times as much dirt as a 2 foot bucket, so it can turn a 1 day job into a 1 hour job.