IMO there is nothing wrong with starting out with either a complete Savage rifle or using an inexpensive Savage action as the starting point for an inexpensive budget constrained build. It is better to shoot in a match and have fun rather than sit at home because someone might look down there noses at your equipment.
As a long time 6.5 X 284 shooter I can state that the main problem is that it is extremely hard on barrels, especially with 20 round strings. A more viable solution, if the work or rifle was inexpensively available would be the 6mm BR or one of its variants (Dasher or BRX). Maybe the 6 X 47 (based on the 6.5 X 47 Lapua). All of them have the advantage of Lapua brass with small primer pockets, and light recoil in a lighter rifle. They are extremely accurate also.
And there would be nothing wrong with the off the shelf Savage F class rifles either. A few have been showing up at local club matches and as they have worked on developement and skills their scores have improved. And kudos to Savage for offering something inexpensive to the starting shooter.
If you decide to roll your own, just keep in mind a quality chambering job, regardless of what chambering you settle on, will make or break your accuracy. You could always get an F Savage and rebarrel later on with a match chamber of your choice.
Probably the best glass on a budget is one of the Sightrons, the glass given the price is excellent, and the erector assembly seems to hold zero well. As with most scopes a 20 degree rail is a must.
There was the salient point that a budget rifle will not necessarily win the nationals. That point is, IMO, irrevalent to a starting shooter on a budget. The point is to have fun and gain experience. There are plenty of folks out there more than willing to offer encouragement and technical expertise.
Will such a rig win a major match, probably not. But it will get you started which is the most important part. If you like the competition later on with a bigger budget you can go for a full on rig.
If I had listened to nay sayers I'd never have started shooting long range, would never have met a bunch of really good folks, and certainly never had as enjoyable a time. Sitting around and shooting the breeze (along with some good eats) is half the fun of a good match.
I would remind some that a few years back, a factory Remington Sendero SF in 300 WM with the addition of a Vais brake came in 3rd at the nationals in Iowa.