I haven't hunted with a No.4, but I do enjoy shooting the ones I have. The factory loads that I have been using are remington softpoints. Because of their round nosed shape, they don't always feed quite right in an enfield though- they feed in my No4Mk1, My No1Mk3 , but not in my No4Mk1*

I've used different milsurps for hunting- A k98, a Yugo M48, and a M1 Garand but won't use them anymore. My opinion on which would be the best milsurp for hunting if not hte best milsurp available would be the Swiss K-31. Its very easy to add a clamp-on scope mount to them, most of them are capable of accuracy beyond that of an out-of-the-box remchestersavage. And best of all, they are fairly light in weight.
Here's one of mine with a clamp on scope mount: