You won't make a good stab of 1000 yards for cheap, but from what I can find you should be able to get setup to have a go.
Of the two, the Remington is the one being used as a platform for customisation, and it's every bit as good as the Howa, so get that.
You will then need a scope with repeatable adjustments, and a lot of range too. Bushnell's Elite 3200 10x40 would do, has 100MOA, reasonable optics and a nice price tag. Or possibly Falcon Optics, but I think you will find the ret very cluttered when stalking.
Don't scrimp on the mounts - get a Picatinny rail if possible, or dece