Several options have been posted...and several good comments. As many have said, first and foremost buy a rifle that fits you best, so go to a store and fondle lots of options before making a selection. I personally love the 308 Win., it is a very accurate caliber and very flexible in bullet options and easy to find ammo for. Plus, if you someday choose to go elk or bear hunting, it too can do that well. Many other calibers to also consider would be the 243 WIN, 270 WIN, 270 WSM, 7mm-08, 25-06...to name a few, but none of them will really outperform the 308 as a good all around round.
I have a couple Rem 700's...love them! But they are older models and I believe they are better then what Remington has been making...but that seems to be changing. Don't think you can go wrong with a Remington, but think you do as well or better for the same money. Many rifles now come with factory adjustable triggers and most have factory free-float barrels that will more than satisfy the average hunter. Consider these options as well...
Tikka - I have a T-3 Lite (in stainless) 270 WSM...fell in love with it the first time I handled it and it shoots like a dream! I paid just over $600. It has a free-floated barrel and a very nice adjustable trigger (trigger really is NICE!...breaks like glass) and is accurate with just about everything I have fed it.
Savage (112, 110) - Also comes with a factory free-floated barrel...buy one with the accu-trigger (really easy to adjust and very nice)...I have 2 and they both shoot very nicely and paid right at $600 each (one also has the accu-stock!).
Browning A-Bolt - another great option...again free-floated barrel, adjustable trigger, very accurte rifle. Hard to beat Browning quality for the $$.
Rugar American Rifle - getting GREAT reviews, I don't own one but have fondled one and heard great things for the $$
Optics...buy good optics...contrary to popular belief one does not need to spend an arm and a leg to get quality hunting optics that are good quality. There are literally dozens of brands people will recommend for various reasons. I personally own probably one of each of those dozens...from Loupy's to Nikon, to BSA (yes, I will admit I own one...it came on a rifle I bought and quickly went into a box on the floor) and Zeiss. I have had good experience with several brands but three stick rise to the top for me based on price, quality, clarity, durability and customer service reputation...
Bushnell's elite (made by B & L)...I have a 4200 and love it! I probably wouldn't have bought it on it's own, it came on a rifle...and I really do like it. I think it is about a $4-500 scope.
Nikon (pro-staff or Monarch) are very good scopes for the money...one can find a 3-9x50 Pro-staff online (SWFA or OpticsPlanet) for less than $200. I own 2 pro-staff's in 3-9x50 and they are both on primary deer guns and love them. Great clarity, high quality, clear to the edge of the glass, and neither have ever failed me. Hard to beat for the $$.
Swift (premier) - My personal favorite optic. Many say you only need to buy one to establish your lifetime relationship with Swift. I currently have 4 of their scopes...including 3 3-9x40's and a 6-24x50AO...absolutely love them! Their clarity is equal to my Zeiss (and was 1/4 the cost), very durable, and great customer service! I had a bad one many years ago on my 7mm...they replaced it no questions asked! Haven't had a problem since. You can find the 3-9x40 or 50 online for between $2-300 (depending on model).
At the end of the day, buy what YOU want and enjoy it! Happy hunting!