We've got similar ground by the sound of it. I use a grey fergie as it's light enough to not mark the ground too heavily. The best 2 implements I have are harrows and a topper so I would put them at the top of the list (you can get self powered toppers for towing behind quads).
My spring routine is harrow, roll, aerate then occasional topping through the growing season to limit weed growth and encourage the grass. We have 4 acres with 2 horses, once they've moved to a new section I usually harrow then top the old one so it's ready for them to return later. I haven't been able to justify buying a seed spreader, any overseeding I do by hand but it's limited to the bare patches.
To keep buttercups at bay, harrow and topping for sure, harrows disrupt the spreaders across the ground, topping keeps the heads down to prevent seeding and allow the grass to swamp them. I've heard lime is good to get rid of them too.
Have fun!
Shaun