I would strongly suggest that to learn and play in the long range bench/ tactical match format you start with a .308. Ammo choices abound from surplus to exotic match rounds. load data is in the excessive range and if you want to go that route optics with drop compensation matched to a load are available. As far as what gun optic combo $2000 leaves the door pretty wide open .
Remington 700 short action get it re tubed with your choice of barrel ( preference would be a lilja palma 30b contour) and a stock of your choosing topped off with a "drop in" jewell trigger group would come in right around 2000 with enough left for a decent scope depending on who does the work. You should end up with a bolt gun capable of taking you the distance. omoymmv but I figure if you wanna play get the right gear outta the gate. There are also any number of company's offering built rifles and there are high end factory rifles that will accomplish these tasks as well Howa, Sako, CZ with the 2 stage set trigger.