In the .30-06, try any decent 150-grain bullet pushed by 50 to 52 grains of Varget. IMR 4064 should work, too, in the same application. An all time favourite of mine, that works well even in old WWII Garands, is 50 grains of Varget pushing a 165-grain bullet. Out of an 18-inch barrel, I'd expect that load to give you between 2,650 to 2,700 feet-per-second. That's a solid .308 level of performance and will drop any deer at any reasonable range.
In the 7mm Remgington Magnum, the notion of "light load" is a bit of a contradiction. However, I've found that Reloder 22 works well with that cartridge. I'd try a premium 140 or 150 grain bullet and begin with the starting loads in the manual. I've usually found that there are two sweet spots. One right up near maxiumum and one a few grains below. Choose the lightest load that gives good accuracy.
For me, the all-time classic 7mm Remington Magnum load, that always works, is 61.5 to 62 grains of IMR 4831 pushing a Hornady 162 or a Nosler 160. That load should be able to do it all, with excellent accuracy. It's not a "light load", but it's also not a super hot load, either.