We would also like to restore the lawn - full of weeds and were thinking or renting a tiller.

This is my understanding of the list of tasks we need to do:

This weekend, mow the lawn (as short as possible),
Water the lawn to make tilling easier.
Till
Water the lawn for 2-5 days to keep the ground wet and aerated.
Put in the scotts seeds+fertilizer combo we got from Home Depot.
Water the lawn everyday for the next 2 weeks

We are hoping to be done with this by mid-oct.

Are we too late in this project? Should we wait till Spring?

Any tips, guidance appreciated.

You are going to till an existing stretch of grass and weeds.

After tilling you will have chopped vegetation and a lumpy surface.

At some point before sowing you will have to rake, level, roll your area.

If your lawn-to-be is on any kind of slope you could be washing your seed to the bottom if you water frequently.

Is there enough warmth in the soil now to get the seed to germinate? Are there enough days before the first frosts bring growth rates right down? Are your early October days generally warm and sunny enough to keep things growing? Are your frosts mean enough to heave new plants out of the soil?

Being foreign I don't know whether you get lasting snow cover over the winter. If you do, then waiting to spring would let your tilled area settle, the chopped plants to either rot or revive, and the uneven patches to show up.

In spring you could deal with any unwanted plants that show up in your lawn area and sow/fertilise to catch the spring flush.