First, reload with .308" bullets. While the name is 303 Savage, the bores on the rifles were always .308" - exactly the same bore and rifling as they used on their rifles for 30-30. Some ammunition mfr's used .311" bullets in early ammunition, but that was apparently to increase pressures and get more velocity with the very early smokeless powders. They all stopped doing that eventually and just used .308" bullets. No reason to use oversized bullets now with modern powders. The 303 Savage case capacity is a few percent larger than a 30-30, and most of us work up our loads using 30-30 starting loads as a base. As you work it up, watch for pressure signs and probably best to avoid hot loads. Tang cracks suck.

I've hunted with an 1899 in 303 Savage using 150gr Hornady RN bullets. Works great.