Hello Liz, Soil settling up to 4+ feet from the home is not uncommon on homes that have a basement due to the backfill soil settling over 10 or more years. Add rain water runoff from the roof if there are no gutters or gutters with down spout discharge that is too short and the problem qets worse. Just about all the soil that is available comes from a farm field that has been regraded for commercial or residential development. Salt should not be an issue, pesticide residues could be a concern if the soil was taken off of fields that were recently being farmed in the last year. The good news is that pesticides today have relatively short lives in the soil. They do what they were designed to and then break down quickly. If the soil has been stock piled for any length of time, it would most likely be fine.
I would ask about using a clay soil as the majority of of the backfill , rather than all black dirt as black dirt will settle and the problem can come back.
Depending on Community codes (something you should check before proceeding) an open ditch may not be allowed. A swale between homes draining to the rear or front of the property is normal and is typically sited along the property lines between the homes. Downspouts from your home and the home next door then drain away to the rear or front curb of the property. You could also consider installing a black plastic drain tile just underneath the lawn that would collect the water and discharge it elsewhere at the rear or front of your property if allowed by code.
The best advice I can give on keeping costs down is to shop around and get the best price you can. I would also suggest you shop this project out to get a clear picture of the actual costs of soil, regrading, seeding, etc. 3 estimates from reliable firms is a good start.
In the meantime, make sure your gutter downspounts are extended far enough out so that roof rain does not return to the foundation wall. Sometimes using that plastic drain tile (without holes) to carry the water away.
Good Luck with your project. Sincerely, Richard Hentschel