Strategy For Fixing Ragged Yard?

We purchased a home (located in plant hardiness zone 6) that sits on a little over an acre back in August of '17. Not long before we bought, a dozen or so trees had been removed from the property, and not long after, the moles moved in. Last year we did have some treatments in summer/fall done in the hopes of curtailing the expanding infestation of perennial weeds. And all the while, the moles kept busy. So between a general lack of upkeep, the areas where trees used to be, and the raised and displaced soil caused by Mole City being established – inexplicably almost entirely contained within my property, I've got some work to do. But before getting started, I need to know where to start...

Below is a screen grab of the property


The worst of the mole benders



At this point I have read through dozens if not a hundred or more short form articles/blog posts/forum threads on the subjects of seeding/overseeding, weed control and mole control, so I have a general idea of what I'm getting into. But within much of that reading exists a lot of intentions for building a pristine lawn. That is not my goal. Essentially all I'd like is as close to a uniform color yard without weeds that grow 2-3 times faster than the grass, and a mowing experience that won't require shock absorbers on the tractor.

As far as the moles go, I have no desire to kill or attempt to drive them to another neighbor's yard, so I'll just live with them the best I can. With that in mind, here's a list of things that I may/will need, in no particular order:
Pre-emergent treatment (service)
Lawn Roller (rent)
Aeration (purchase pull-behind or service)
Slice seeder (rent)
Tall Fescue seed

Although I understand that fall is the recommended time to seed grass, I'm thinking I'll have far too many leaves to contend with in that time of year, so I'd prefer to go with springtime.

So with all that's mentioned above in mind, does anyone have tips/thoughts on how I might be successful in trying to get things under control, particularly without going overboard with expenditures or things that I don't need to do? Thanks!