I would start with the scope. I'd look at Nikon Prostaff (though I'd step up to the buckmaster line if at all possible), Vortex Diamondback (though Viper if you can afford it), Bushnell Elite 3200 if they are still in stock (though they are discontinued so watch the warranty), Burris fullfield II, Sightron SI (though SII if you can afford it), Leupold VX-II (I'd personally pass on their rifleman and VX-I line), anything Weaver, maybe if the budget were real tight a Mueller or Pentax though they would be last on my list. These should all be as good of scope as you can get for the money.
Remember, you spend the entire time looking through the glass. If the scope stinks, it's no fun. You still need a nice rifle, but don't go cheaper than these scopes. A lot of them can be had for $150-$200 which still leaves a bit for the budget. I've tried most all of the cheaper scopes or scopes for similar money with big features. All of them were a let down. Bought a few from the list above or nicer and all but one have been nothing but great and that one is still leaps and bounds better than the cheap stuff. While you may not like the bigger entry price, by the time you buy two or three junk scopes you could have bought yourself a decent one to start. If you spend $300-$400 on the rifle and $200 on a scope with no more than a max of 9x magnification you will have yourself a decent combo. Don't get sucked in by big magnification and a cheap price. The two don't go together well. A quality scope with low magnification will be more enjoyable than a cheap scope with high magnification. Trust me on this one.
As for the rifle, it seems you have a decent plan. I would strongly suggest .223, then .308, then .30-06, then everything else in that order based on ammo cost and availability. By about 1000 rounds shooting .223 you will have saved as much on ammo as that scope listed above cost.