I can only second 1500Varmint, either a Tikka, or a Bergara would be a great start. I'm kind of partial to Bergara because the magazines are the basic Magpul AICS and friendlier to the wallet, and bexause of the Remington 700 footprint on the Bergara.
The Sniper's Hide APO Saber 700 would be another great option if it is within your budget.
Builds tend to take a while to get all the parts and also tend to run higher, plus there are some parts you are better off ordering together. If you are completely new to bolt actions a near custom factory rifle like Bergara and Tikka are a great way to learn and you can still tinker around on them and customize them to your liking via different stocks, triggers, etc.
Sometimes builds can take years to complete while the near custom factory rifle will get you out on the range learning which features you like and which you might want to change when you finally do build that dream custom rig. Without that knowledge that build can easily turn into a super expensive FrankenBuild with flaws that will keep you dissatisfied and the wallet permanently drained.
I generally tend to agree with buy once, cry once but sometimes the budget prevents flights of fancy. In that case it is always advisable to get a decent budget option and buy the best quality glass and things like bases, rings, bipod you can afford so you can transfer them to that build once you are ready to take that step.
Just my two cents worth, you can take it and run with it, or you can tell me to "keep the change", either way I'm fine with it. Just my observations about builds, from personal experience they usually don't turn out as economical one part at a time as it sounds, or we make ourselves believe. My wife would probably tend to agree.