re: Do I need to till before putting down new grass?

As ronk mentioned, with new topsoil there’s no need to till it.

If you want to mix in any amendments or anything like that, you could, or if you’re only going very shallow with top soil, it wouldn’t hurt.

I killed and tilled mine when I planted, but I was not bringing in any soil, and needed to really break up the compaction to plant the seed.

Are you going with sod or seed?