Sort of hard to say without bigger pictures; picture as in a photo of a larger area of lawn, and picture as in your ultimate goal. Is this property new to you? You said that it has been neglected, so, if this is your first shot at it, I would start by simply mowing it, and keeping it mowed. When my lawn goes too long between cuts, I see a lot of different looking growth, and if can look pretty neglected sometimes, but gets back to normal after a cutting or two. Even some of the grasses if let go to seed take on a bit different appearance. You mentioned low spots; do you know why they are there? Septic field? Maybe previous owners had a garden there? Newer lawn still settling? Erosion? Maybe grading changes are needed? Or maybe it just needs some fill in a few areas? If so, how much? Not the least expensive way to go for larger volumes, but you can buy top soil at your local garden center or big box. Aeration is seldom a bad idea, and, depending on how much area is involved, you can probably rent an aerator locally. Well, a few thoughts anyway.