You can't go wrong with a Tikka in my opinion...for the money they are a great rifle...adjustable trigger is crisp and breaks like glass and is easy to adjust; accuracy is really good out of the box; bolt is smooth as butter; detachable magazine is a plus. I have a Tikka T3 Stainless Lite in 270WSM and really love the rifle for all of the reasons above.
That being said...other good options out there include Browning A-Bolt...also adjustable trigger is nice and crisp and easy to adjust; detachable magazine is easy to use; good accuracy out of the box; and can be had in a nice wood stock if desired. I have one in 25WSSM and am very impressed with it's accuracy.
Savage Model 10's and 11's are also another good option...again, very accurate from the box; very nice adjustable trigger (if you get one with the accu-trigger); detachable magazine is available in most versions; accu-stock option is a plus for upgraded beaded stock options...I have a model 10 in 308 and a model 11 in 7mm-08...both shoot very well and like most "food" I feed them.
Weatherby Vanguard (Howa 1500) is also another good low-cost option. My daughter and niece shoot Vanguards in 243 and they are very accurate out of the box, have a nice trigger and handle very nicely.
You most certainly can't go wrong with a Sako...I own a Sako, but it's a Finnwolf (lever action)...so can't provide you any personal experience with them. Remington 700 and Winchester Model 70's would also make the list...I have several 700's but they are all older BDL's and a onder 70 (pre-'64)...so again can't give any person input on never versions of these rifles. I am not a big fan of Ruger bolt action rifles...they are durable and certainly reliable and will get the job done, I just despise their crappy factory triggers.
All of the above will serve you well.
Optics options in your $500 budget...
- Nikon Monarch (clear as an Zeiss for less $$). I have one on a new build that is just about finished and am very impressed with its clear optics!
- Nikon Pro-Staff (will certainly serve you well, but you can see the difference side by side with a Monarch)...I have a couple and they have served me very well in the field.
- Swift (very good scope for the money, American made glass and components, great warranty, very clear and well worth looking at)- I have several, some for over 20 years and all have been trouble free
- Bushnell Elite 3200/4200...have one on my 25WSSM and a 243 and they are amazingly clear and is well built.
Invest in good rings/bases from Warne (my personal fav...Made in USA and steel!), EGW, Millett or Lupy