I currently own a few rifles, and I have owned alot of others and shot many more.
Having said that, I would have to say that the most fun rifle I have is my Finnish M-39 Mosin Nagant. It is extremely well crafted, steeped in history, and deadly accurate. It fires a powerful, inexpensive round and I can pop clay pigeons with it at 200 yards. Mind you, my eyesight sucks and I can just barely see a clay pigeon at that range, but I can hit it. At least with that rifle. (Though not with any other to date.)
I can't really explain it. The heft and balance are just perfect for me.
It is not only an instrument of fun, but also an instrument of war. The Mosin Nagant started service in 1891 and has been in use somewhere in the world constantly ever since. It has seen combat in three centuries. Over 100 years, and there are no doubt still a bunch of them seeing use in Afghanistan or somewhere as we speak. You have to be doing something right to make it that long.
I love all guns. I love the simplicity, reliability, and durability of the AK. I love the FAL because it is just an awesome combination of a powerful round and firepower. I love the Garand, Springfield, and Enfield for their toughness and for the role they played in serving freedom. I love the AR/M-16 for its ergonomics and for the memories it brings back when I hold one. I love the Winchester and Marlin leverguns because of the history behind them and the fact that nothing has replaced them and nothing ever will. (Please note that I can't afford all of these rifles, yet.)
But for me, when I hold that M-39, there is just something about it that I can't explain but that I know is there. It is the mechanical equivalent of a soulmate.
What you have to do is just experiment until you find the one rifle that gives you that feeling.
I suggest you start with an unissued M-39.
www.gunsnammo.com