The Hornet is a fine small game round, and was the first commercial varmint cartridge. It is a little finicky to reload, but considering the cost of new factory ammo, its very worthwhile.
The Hornet is the lightest standard centerfire round, and bridges the gap between the .22WRM and the .222/.223 class rounds.
The New England Handi rifle is a bargin basement gun. If you get one with a decent trigger, they can be quite accurate, but they are not in the class of a Ruger or an Anshutz.
All else being equal (and it almost never is) bigger bullets tend to work better.