You can't go wrong with a .30/06, its my favorite cartridge. But you could go wrong by choosing an ultra light rifle if you want something for regular shooting as well as hunting. A .30/06 that weighs less than 7 pounds and comes with a hollow plastic stock will leave you punchy after just a few rounds of 180 gr factory ammo. On that note, if you intend to get into handloading, you can load your ammo to fit your comfort level, then over time, you can increase the power as you become conditioned to it. I loaded up some 130 gr bullets at 2600 for both my grandson and my nephew, and both of them found that the ’06 could be a pleasure to shoot. My nephew took a couple of deer with that load.
With a small budget, the advantages of purchasing a used high quality rifle cannot be over stated. $400 won't get you a used pre-64 M-70, but it will get you any number of Husqvarna M-1600 commercial sporters. These rifles are great quality and if they were still manufactured today would command big dollars.
Tradex has a wide selection, perhaps a bewildering selection is a better description of their online store. But if you take your time and browse through the pages you'll find the right rifle for you. You can take the rifle’s condition from Tradex to the bank, if anything it will be understated. If a rifle needs work, they tell you. One of these rifles is a much better investment that the bargain basement selections offered on the North American market.
You should invest in a good quality recoil pad like a Limb saver or a Decelerator, just to make shooting those long strings a little more comfortable, particularly in warm weather when you would shoot without wearing a jacket. The proper fit between a shooter and his rifle is all important, and the addition of the recoil pad presents the opportunity to take that step.
So there you go, you've decided on your cartridge, and now you are a step closer to a semi-custom rifle, even though its on a small budget.