Nickel plated ="pretty" round that doesn't tarnish on the shelf. For auto's, it may help loading and extraction due to the smoother finish, but is useless in a bolt rifle.
For PD's at that range, the bullets you selected should be fine; the ballistic tips should vaporize them. Don't overlook Sierra Matchkings either; they are basically a hollow point with a thin copper jacket. If you wish to go into longer range, the 100+ with high BC's will be best.
As far as a decent reloading setup, do not go with the Lee kit unless you cannot afford better. You will regret it later, as you will get "hooked" on reloading, and in some point in time, that cheap steel press will break, and you will upgrade to an electronic scale. I speak from personal experience.

The only good thing about that setup is you receive everything, with the exception of dies and shellholders, to get started.
Some may tell you to purchase a progressive press, which is fine for mass producing rounds. I only use mine for pistol rounds, but for all of my "accurate" cartridges, I use my single stage. I am slightly anal about case prep and measuring powder weights, but am rewarded with 1/2 MOA or less groups if I do my part.
By the way, is your rifle the Winchester Coyote with the stainless barrel?