The optic, I see as a foregone conclusion. There are way fewer inquiries about using really cheap, shitty optics these days than there were 10 or 15 years ago. And to be honest, there are several well-known optics in the sub-$1k price range that I would happily use from 500-1000 yards. My next optics purchase is probably going to be a Nightforce Benchrest model, but that's beside the point The other thing is, I'm less inclined to advise spending more on optics on P-F than I would other places, as the culture already leans towards non-shit glass.
Ammo--*shrugs*. It wasn't in the scope of the question, but yes, I would acquire loading equipment before I spent on a very pricey rifle. There are really good factory options for good target ammo, especially in 6.5CM. To my way of thinking, the economy of both quality factory ammo and high-quality reloading components is the biggest reason to choose that cartridge or the Grendel.
So! Budget action in a pricey chassis! Not "good", because there are plenty of really good budget options, but pricey. Putting a lot of money into a chassis means wedding yourself to the inlet. If you want to get out of it later, you're going to lose a bunch of money selling the thing (although it's better than a traditionally-bedded stock), especially if it's built for some rifle that the caviar rifle set doesn't like. To an extent, you can avoid this by going from a Remington 700 action to a clone custom, but now you're limited to 700 clones, and not every chassis' 700 inlet supports clone actions without modification. And to be frank, I don't think that most shooters really need all the features a chassis offers. If you can attach a good bipod and a cheek riser, you've got 90% of what an adjustable chassis will do for the average guy. I love mine, but I also know I'm not using half the capability.
A custom action, on the other hand, does a ton of stuff. It'll be smoother to operate than a factory action. You'll have a nice, easily-removable, ultra-reliable extractor, and either a choice of bolt knobs or a threaded handle. They're available with milled rails for optics, and you can count on everything being squared-up, centered, and perfectly threaded. You can install a good barrel and know that whatever happens, it's not the action's fault. The entry-level actions really offer a good value when you consider what it would cost to bring a factory action to that level. The Defiance Tenacity is a steal.
I would dip my toes with a basic 700 or Model 10 with a heavy threaded barrel, and a Vortex Diamondback Tactical scope. If I decided I had to have a chassis, the MDT LSS Gen 2 or LSS-XL are both quite reasonable. If I thought about spending any more than that on a chassis (MDT ACC or ESS, Masterpiece Arms, etc) I would really make a longer-term plan about what I wanted.