30-06 is a great round for 600-700 yards. Since you're not wanting to hand load, grab a few boxes of "match" type ammo and see which one your rifle likes best at 100 and 200 yards. The tighter groups the better. Every rifle/barrel will be different. I'm sure you know this but just be aware that any variance in shot at 100 or 200 yards zero is going to be magnified at your desired 600-700 range. Once you find the "right" ammo, don't change a damn thing on your rifle or you get to start over. (at least that's how things have went for me----I haven't shot much the past few years due to many circumstances)
Optics are a total Ford vs Chevy vs Dodge thing. I'd pay the needed amount and get something you like rather than buy 2-3 "maybe" units that might work out and have some "meh" stuff kicking around your man cave. I would suggest your price range would be at least $400 and up. I've seen folks using Leapold, Vortex, Bushnell, Zeiss, etc (even Tasco) have good success. Something in the $700-1200 range would get you something that would be comfortable to use and have a reticle you like.
Edit: Oh, rifle... You could use exactly the same weapon you have. I have been ogling the Tikka rifles of late. Not sure if you're into those or not. I bought a new Rem 700 6-7 years ago and will likely pass on buying one of those again. They're not bad but definitely not what they used to be. My brother has a Browning X-bolt (maybe it's an A-bolt or something?). That's a nice weapon as well.
More editing: There are MANY calibers that will shoot like a laser if you wanted to get a little more exotic. 6mm and 6.5 variants, .20 cal variants (.220 Swift, 22-250 and .204 Rugers can be cool--I'm sure there's a bunch of wildcat variants along those lines that I don't know anything about), good old .270, and .30 cal 7mm unit will get you to your 700 yards with ease. Some of the really "hot" calibers will wear a barrel down pretty well/quickly.
Interesting article on some .20 caliber stuff if you're interested. I personally wouldn't use these for deer but it'll let you know what you can do if you wanted to quit traveling and get another job to pay for all the cool stuff
https://www.6mmbr.com/20caliber.html