The Remington 700 is a great gun for the money. I've been looking at getting the 700 SPS Tactical in .308 myself. I'm not sure if it's a good deal because the gun market is a lot different in the US than Australia.
If you're mainly going to be taking it to the range the .308 is a solid choice. I'd say it's one of the most fun calibers to shoot but it isn't exactly cheap (around $0.50 USD per round, before the current ammo shortage). You might even consider downgrading to a .223 if you're only going to use it for target practice (still a fun caliber).
As far as going to higher calibers like the .300 Win Mag or .338 Lapua-- don't unless you can afford it. Win Mag is about $1.50 USD per round and .338 lapua is about $8.00 USD per round-- for the price you might as well buy a .50 caliber.
The .308 is a proven caliber and can take down most game you're likely to encounter short of a cape buffalo, elephant, or a body armor-wearing polar bear. It'll do great on the range and also for hunting.
TL; DR Good gun, great caliber, get the gun, get good at shooting at a distance, and have fun!
P.S. As for the scope, I can't say I've heard of it. You might want to do a fair bit of research into it as a long-range rifle normally needs a scope of the same price (just a rule of thumb). The scope could make or break the deal. You can always get your own scope but if you're buying used you can either get a great deal if a quality scope is included or get thrown for a loop.