The true cost of shooting is not in the rifle you choose, but in the ammunition it consumes. The first question you should ask yourself is, "What is it for?" If you intend to be exclusively target shooting, you don't need a rifle chambered for a round that is as expensive to shoot as the 6.5s or and .308s. Many will champion the .22 rimfire as a first rifle due to the low cost of the ammunition, but my opinion differs in that I think a .22 rimfire is a beneficial learning tool when used in conjuncture with a centerfire, but that it creates a mental barrier against the centerfire rounds due to the disparity in cartridge size, when used in exclusion to a centerfire rifle. Once a mental barrier has been well ingrained, like a flinch it takes much time and ammo to overcome it. If you have to pick between a rimfire and a centerfire as a first rifle, choose the centerfire, preferably a .223 for which less expensive surplus ammo can still be acquired, and consider handloading at the same time that you begin shooting.
If the rifle is intended as a big game rifle, the cartridge choice at one time was quite simple, since surplus .303, 308, and .30/06 ammo was all commonly available at low prices, and the FMJs could be replaced with soft points of equal weight without needing to tweak the powder charge. Today if you live in an province that mandates a .23" or larger diameter round for hunting, the only inexpensive surplus ammo you'll find is 7.62X39. Currently rifles chambered for this cartridge are made by CZ, Zastava, Ruger, and Howa. Is it the perfect all around big game cartridge? No that title is owned by the .30/06 in North America and the .375 H&H in Africa and Asia, but the 7.62X39 is a good introductory hunting round suitable for deer, antelope, sheep, and black bear. One fellow I know dumped a large moose with his 7.62x39 Ruger 77, and it only took a single shot. Do I consider it a suitable round for game that weighs in excess of half a ton? No, but it is suitable for game that weighs up to 500 pounds, that can be shot at ranges up to 200 yards. When loaded with a 150 gr pointed bullet a muzzle velocity of 2150 fps, sighted 2" high at 100 yards will zero about 150 yards and be about 4" low at 200 and 8" low at 230.
These figures are not particularly inspiring when compared to the 6.5X55, the 7X57, or the .308, but they are suitable for medium sized game taken at modest ranges. The key is that this is a round that can be fired frequently on a tight budget, and won't beat you up while you are learning the basics. With a current price of 25 cents a round for surplus ammo and the larger rounds costing about a dollar and a half each when loaded with soft points, you can fire 6 rounds of 7.62x39 for every round of the others. If you purchase some handloading tools, you can replace the FMJ surplus bullets with soft soft points, or cast lead bullets and still have affordable ammunition. Embrace this idea and shoot that rifle until you can make it do what it was designed to do when shooting from field positions. Then you can take up hunting with it. Shooting rabbits with a centerfire hunting rifle is a good way to hone your skills and can be done through much of the year.
Several of the rifles chambered for 7.62x39 come with factory iron sights. If you can put off purchasing a scope, that would probably provide you with the cash needed to acquire the modest handloading tools you need to get started (a Lee "C" press, Lee dies, a shell holder, a kinetic bullet puller, and a set of Lee powder measure spoons) or it might allow you to upgrade to a better rifle than you first considered. Again keep in mind that the true cost of shooting is more the price of the ammo than it is the price of the rifle.