Chocolate lab, golden lab, meth lab, whatever. :-)

For our locale (I'm eastern PA, so close enough), and a soon-to-be sunny environment, and somebody who seems to be in the beginner range, I'd recommend an off-the-shelf tri-mix.

Or, something with all three major grasses in it--rye, fescue, and Kentucky bluegrass.

Brand doesn't really matter, per se, but I'd look for something with 0 noxious weed seeds in it, and the lowest percentage of weed and other crop seed in it you can find. I generally don't recommend the Scotts brand because that's overpriced and not very good.

If you were to go one step higher, I'd look for something with more bluegrass in it, and with Midnight bluegrass in the mix. The grass will be darker, not much harder to care for, and have better ability to self-repair damage. And more expensive, of course, but not all that much.

I wouldn't recommend the elite mixes in this instance, they're going to require care levels you're probably not interested in providing. They're for hobbyists. Eventually, like mine, they can be taught to stand on their own roots and do their thing, but it does take a while.

First, get rid of the tree, and get the soil replaced and leveled once the roots are out of there. Professionally, I presume, as mature trees are nightmares to do yourself.

Second, I'd probably get a soil test. I'm familiar with the soils of South Jersey and the locales around the Pine Barrens and would definitely recommend one through Logan Labs, particularly in a soil a tree just was in and where unknown soil just got dumped.

The correct time to seed will be whenever evenings just start to cool down, usually around August 15th-August 25th for most of us around here. It's that evening when you stand outside and say to yourself, "Summer's starting to end." Or, earlier than most people think. It gives the new seed a solid week of hot weather to pre-germinate, a week of slightly cooler weather to germinate, and a few weeks of cooling weather to grow in strongly.

For sandier soils--like you have--topdressing the area might be a good idea, but it's optional. 1/8th inch to 1/4" of peat moss (the stuff in the bales) is perfect. Compost is also perfect.

Water three times daily if you can, for about 7-10 minutes at a time. Once in the morning, early afternoon, and evening. Seed must stay damp all the time. That's why the top dressing.

Fescue and rye will sprout in 7 to 14 days. Don't stop watering, bluegrasses require 28 days to fully sprout and you want the bluegrasses.

At Day 28, cut back to watering one time per day for about 20 minutes or so if nature isn't watering that day.

Two weeks later, water every other day.

Two weeks after that, move to every third day. The weather is getting colder, so check the soil. If it's consistently wet, you can even go longer and, of course, rainfall counts.

Two weeks after that, it's November first and you're probably close to done for the year, but if it's still warm, keep watering. Twice a week might still be necessary.

Note I didn't mention feeding. Depending on your soil test, it might or might not be necessary. Seed doesn't really need much in terms of feeding the first thirty days and, other than that, try to stay off the lawn as much as possible (the dog is fine).

Feed once in November for winter to carry it through with a nice high-nitrogen food. By then, the roots are grown in enough for it to absorb the nitrogen and for the N not to get lost into the water table.