Need Opinions. Buying a Target rifle

I am new to the gun scene, particularly the rifle scene.
I have a range nearby that I currently go to with my little 22 long rifle. Its good for the kids cause the rifle has little to no kick and its great for the 50yd range.

I also go to a range in Yuma ( when I work out there) that has a great outdoor target range up to 800+ yards. Not that I need something that shoots accurately up to 800+ yards but I am looking at something that will be accurate and fun to 400 yards and not too expensive to shoot.

I have been looking at the Remington 700 VTR and other 700 models and have found a few places with decent pricing. Outside of that gun ( which I hear is a good accurate rifle), i have only read about other guns and have not held or fired anything else.

My price range with gun and scope and any upgrades is $1500-$2000.

My questions to you rifle owners:

1. opinions on .223 ammo vs. 308 vs 30-06 . Which one give me the best cost to accuracy ratio.
2. Will the .223 shoot up to 300-400 yards? my local range only lets you shoot .223 or less ammo on the rifle range.
3. I am in california and other than not having your gun fully auto or a suppressor, what other laws are in place that I need to know of with a rifle like I am buying.
4. Any other suggestions for a rifle and scope that you would suggest.

Thanks in advance