A lot of different, and a lot of really knowledgeable and experience people, much more so than myself, on here that will help you. Cool thing about Remington's, they have **** near every aftermarket products you can think of available for them. Don't feel like you need to do everything at once, or everything at all. If it were me starting from where you are, I would first off replace the stock on that thing. I have bought two 700's in the past few years, an SPS tactical and a Sendero. I put McMillan Game Scout on the Sendero (I think it was about $520 after adding a second stud and shipping) and a B&C Tactical Medalist Style 3 w/ "Hook" (About $230) on the SPS Tac. I should say that the Sendero already has a good stock on it, I just was not a fan of the wide forend and palm swell. I think the SPS has an adjustable trigger on it, so lighten that puppy up and tune it to your desired pull.
Spend some time trying different brands of ammo out and see what one your gun likes best. I would say quality glass is something you will want to invest in sooner than later. I ended up going with the Vortex Viper PST (the big boy of course), and love it. The glass is outstanding on it, and the clicks are super accurate. All the suggestions that were made on here are good ones, and ones that you should consider...If you arent happy with making a few minor changes. I personally was on a strict budget when I was choosing my guns, and its components. I wanted basically the most accurate gun I could afford. My Sendero and my SPS tac both shoot .5 MOA with me doing my part. I think expecting accuracy out of the SPS in a 30/06 at 500 is very do able. I would adjust the trigger, replace the stock and get a good piece of glass with a solid base, and asses what you would need from there.