The new Ruger Precision in 6.5 if you can find it at the right price. Currently the 6.5's are still in stupid money land since dealer on them is around $900~.
Sendero's used to be a good choice but prices are up there these days. Remington makes a HB LR rifle in decent stock for $600-$700~ I picked up a bunch of them and parted out a while back in the $600 range. I got $225/stock which put me in the $375 range pre heavy barreled action. Add a $700 AICS stock to that and your shittin pure gold. Remington Long Range Rifle
I started my FIL in LR shooting. I bought him a Remington SPS Tactical. Traded around and got him an HS stock for next to nothing. Put a MK4 on it and 20MOA Badger rail. Wasn't cheap by the time it was said and done but was done cheap enough since we bought everything except the rifle used off the used section of snipers hide. I.E. Used MK4 scopes in the $700-$1000 range for scopes that go for $850-$1500.