Get some range time in, and get used to the way the sites are set up on the 44. You can find alot in various websites about the bayos effect on accuracy, and the way the sites were set up as a result.
I have used one, and will go contray to all here, and not recommend it, unless you get proficient with the rifle, and its safety. Its the safety and its clumsyness that is the downside for me.
As far as ammo stick to the better stuff for hunting, alot of the cheap crap is just that, crap. Core/jacket separations being the norm for alot of the low end pap. If you can get the Norma, the 150 and 180 loads are great, and bullet construction is well up there. Look around though, you may be able to find some Sako loads (they used to do 7 at one time), or even some of the Lapua stuff (though don't hold your breath). If you want to do a good job I would suggest either the Norma, or to reload. You can get new Lapua cases, and a variety of applicable bullets with ease.
From a reliablity perspective the M44 is light years ahead of alot of the clunkers you see mentions in this forum, only its safety being cumbersome.
Still the best user friendly gun design for 'modern' era military bolt action.