A .223 for moose!!?? That sounds like the kind of advice you might get from Cabelas. The .30/06 as it happens is perhaps my favorite cartridge, but in a light rifle it might be a bit more than a new shooter can enjoy, and unless you intend to delve into handloading at the same time as you begin your introduction to marksmanship, which if you can manage it is a good idea. The handloader can choose the power level of his ammo, and his home made ammo is more affordable than factory ammo, in that except fort the initial investment, he can deduct the cost of the brass from his ammunition. But handloading can be started anytime down the road, as can the purchase of a scope, a sling, and so on.
Since cost is a big factor, the advice I pass along to new shooters is to look through the pages of quality used rifles on the TEC Tradex Canada site, whose link appears at the top of the page. Pay more attention to the rifle and less attention for the cartridge it's chambered for. The .30/06 cartridge is a common chambering, but any cartridge from 6.5X55, Cabelas carries ammo for it, to the .30/06 will be fine, and chances are you will really enjoy shooting the mild mannered 6.5. Other cartridges to consider are the .270, 7X57, 8X57, and the .308 Winchester. Avoid magnum rifles for now, they will be more costly to shoot, and will be more difficult to master.