I'd agree with nhm16, add 7mm-08 Rem and possibly 6.5mm Hornady Creedmoor. Despite what many say there is nothing ballistically between .260, 6.5mm HC and 6.5X47L, and unless you're into a benchrest quality rifle, nothing accuracy-wise either. All are good cartridges, light recoiling, and ballistically efficient.
The big pro for 6.5X47L is the quality of the out of the box Lapua brass, altho' the con there is its price. However ..... remember, this case takes a small rifle primer and you will likely crater them / suffer 'blanking' with your Remy 700 firing pin / bolt at pressures and MVs below those available in a rifle built on a custom action. You can have this sorted, but it's an additional expense.
.260 Rem and 7mm-08 Rem downsides are brass, but you can use Lapua .243W necked up or .308W necked down, and they have the large primer so no problems there. (The brass is also cheaper than 6.5X47L even when from Lapua.)
If you go down the .260 Rem route, you need to think about bullets and throats before the build. The factory version is a bit of a compromise. There's a top gunsmith over here in the UK who builds very expensive sporting rifles and favours this cartridge. He goes for a very short throat to suit the 100gn Noslers - Ballistic Tip for varmints, Partition for deer, the latter developed especially for this cartridge. He says the Partition will take a Scottish Highlands red deer stag cleanly, although these are not as large and heavy as the European equivalents.
In the sevens, 7mm-08 is a fine multi-purpose cartridge with excellent long-range ballistics. You could also go for the 6.5-284 or its parent .284 Winchester, necking Lapua 6.5-284 Norma brass up for the latter if desired, or using Winchester with a bit of sorting / preparation. 6.5-284 has barrel life issues though, and while the .284 Win is better, it's obviously going to be shorter than with 7mm-08 Rem given the larger case and powder charges.
In the Rem short action, and with varmint shooting in mind, both versions of the 284 need to be fairly short-throated to suit the magazine led 2.9" or thereabouts maximum COAL, also to suit 100-120gn varmint bullets. That means the 6.5-284 Winchester (not Norma) version of the former, and more or less standard .284 Win for the latter, not a custom long-throated version designed for heavy bullets in a long action. So chambered, heavy deer or target bullets have to be seated very deeply, but the .284 Win works very efficiently with 140s and 150s if they're man enough for your deer hunting.
Laurie,
York, England
