Well fun to shoot, to me, would require:
A) low recoil. Something in a 243 might be a real good e-z kicking choice. If you are not yet a big hunter know that a 243 will take anything up to and including deer (legally) - which includes rabbits or coyotes or skunks or whatever as far as one should likely take one. B) lots of different loads to try - 243 fits the bill there too. Everything from 55 to 100 grain. Something in there for whatever the purpose. C) Exciting- get something with a good trigger right out of the box. I might recommend a CZ 550 because of the set trigger. Push the trigger forward and it clicks, putting it into 'set trigger' mode. The lightest force will trigger it and that makes for awfully good target results and is just a hoot. You don't have to use the set feature and can just pull it like a normal trigger if you want - good for most hunting. They are well built and come with rings. They are not heavy but not as light as a lot of others which, combined with its excellent decellerator recoil pad, would make for very pleasant extended shooting sessions. Nothing wrong with the Rem's (I own and love mine) and the new Winchesters seem very nice. Tikka is a great choice if you like them and the triggers have a fine reputation -just maybe not as easy to top load. Weatherby's can be a real bargain as are Savage. Ruger is made in America and also comes with rings. If you decided a little more power is needed for the longer ranges I would go up to a 25-06. That is starting to burn some powder but recoil is still doable for about anyone. Going up to a 270 or 308, especially in a lighter rifle, while certainly manageable and even comfortable with experience, can be detrimental to a newer shooter and just plain not as fun. Whatever you do D) do not buy a caliber bigger than you want\need. Biggest mistake most people make is buying a magnum or some heavy kicker only to secretly hate using it. The guy who shoots comfortably will ALWAYS shoot more and consequently, shoot best. Does this help?