Early game you can also go to Broc Flower Cave (far south of Novac) to retrieve the Ratslayer. A fully modded unique Varmint Rifle. Watch out for the rats.
This is what I've done so far for early game snipering. Came across this before a hunting rifle even because im a nice guy and didnt wanna kill the ghoul earlier on and take his. Guess I should have though, lol.
It's not as strong as a sniper rifle, but dude, the scope is nice to look through, headshots kill all your non-super-badass mobs (meaning, deathclaws

) and it looks sweet in hand. Sometimes you gotta trade function for FASHION right?

Plus you can repair it using ghetto varmint rifles that cost nearly nothing.
The actual sniper rifles are both rare, and freaking expensive. Meaning you will either need to pay to use it full time, or, have a softer backup for other cases. The ratslayer is a good backup sniper when you cant afford the sniper, or, can't find one yet

Plus the cave its in is easy-mode to clear