You have a big project. First thing is to find out what soil is
already there. Many areas have agricultural services that will analyze
soil samples for a small fee. Check the phone book under county
listings. If the soil already there is ok, that is going to save you a
lot of bucks. You need at least 6 inchs, preferably 9 of good soil.
Paying for topsoil to cover an acre isn't going to be cheap. Whatever
you go with, have the PH checked, which is very important with
disturbed soil or new top soil. Apply lime to get the PH adjusted if
needed.

You also need to get rid of anyything growing there just prior to
seeding. That likely means you'll need to use Roundup (glyphosate)
about 2 weeks prior to seeding.

For grass, a mix of the newer dwarf type tall fescues and blue grass
would likely be a good choice. You can apply it with a slice seeder.
You also should put down a starter fertilizer.

For watering, I agree, a large rotary is the way to go. But what are
you going to use for a water supply? You need to be sure you have
large enough piping to supply a head with the capacity you're talking
about. I don't think I'd rely on moving two of them around somehow,
it's just not practical. For the cost of some extra pipe, and heads,
I'd rig it up so you don't have to move stuff around. Even working the
valves is a major pain. In the first couple weeks, you want to water
it for short periods to keep it constantly moist. That means several
times a day. I'd wait till early fall, which is the optimum time to
establish a new lawn. Hopefully, you'll get enough rain then to help.

Hydroseeding is a good way to establish a new lawn, but it ain't gonna
be cheap either. It's seed, fertilizer and hydraulic mulch sprayed
onto the surface. You could get some quotes, but you'll find that DIY
with the slice seeder, which you can rent, is going to save a lot of
money.

When you get to cutting it, it's not very practical to bag an acre.
I'd use a mulching mower. It's also more beneficial to the lawn to
return the clippings. The only advantage to bagging is it does leave
it looking somewhat nicer.