What are you considering to be cost effective?
What do you mean by "benchrest rifle?" Are you talking about a heavy rifle you can enjoy firing from a bench at targets for pleasure, a bench rifle for colony varmints, or about a competition ready rifle? If competition, which type and which range? There's a big difference in precision tolerance between these two options, and of course, if you're talking competition, your WEIGHT matters, so recommendations for different action type/brand would change based on which class you're after. Cartridge will also change depending on whether you're looking to compete or not, and at what range.
Factory Savages and factory blueprinted Remington's - or cheaper custom Remington clones - can do well for recreational shooters, even keep pace in some light rifle competition, but you don't see many of them on highly competitive firing lines for a reason.
.22-250 doesn't even begin to smell my list of choices for a competitive benchrest rifle. A heavy varmint rifle fired from a bench, sure, not a competition rifle.
Since you're asking the question about buying a barreled action, it sounds like you're going to be best served by calling a smith or a barrel & action maker (shilen, for example) or other custom gun builder (McMillan, for example) and talking through your wants. You can likely find a rifle which suits your needs and won't involve a lot of technical understanding for selecting your components on your own. They'll already have that knowledge.
