1.) adjustable sights on the rimfire......you may have 4 bricks now, but if you are using it to make meat, you make go through that in a hurry......if you come across another "brick" via barter or trade, it may not shoot to the same point of aim. Better to fire off a few rounds and adjust the sights.
2.) make sure said centerfire will fire with HP ammo.....quite a bit more prevent today than ball (and a better 'stopper' in most cases).
3.) spare parts kit for both, if possible. Also, make
sure that the spare mags WORK, esp. if they are aftermarket.
4.) cleaning rods/supplies for both.