Bottom line: If you want a rifle, get a rifle cartridge. The logic in buying a common cartridge to keep ammo cost down is flawed.
Here's a classic example:
A politician in excitement asked an engineer, "Can it be done? Can we do it?"
The engineer thought for a second and said, "Well, yeah, we can do it..."
And the politician ran off in a rush to spread the word, while the engineer finished his thought, "...but it would be REALLY stupid if we did".
Sure, you CAN kill a deer with a .357mag, quite effectively in fact, but does it make sense to spend money on a rifle specifically for that reason? No, not in my book. At 100yrds, a .357mag is STRESSED to perform, period. Why would you intentionally chose a marginal cartridge? I'm not saying a .357mag isn't a "deer cartridge", as I have dropped half a dozen deer with .357mags, and my wife uses a 2.25" Ruger SP-101 as her close range deer medicine, but nobody is going to say it's a "great deer rifle".
You'd be FAR better off by picking up a .30-30win or .308win, or any other of a dozen inexpensive RIFLE CARTRIDGES instead of a MARGINAL .357mag rifle. The .44mag is FAR more powerful than a .357mag, and as much as I LOVE the .44mag, I'd make the same statement. If you want a rifle, get a rifle cartridge.
I'm all for having a common cartridge between a revolver and a rifle, especially if you are trekking out horseback for weeks on end and carrying everything you own in your saddlebags.
If the above statement doesn't apply to you, then a common cartridge doesn't make much sense.
Personally, I LOVE the .44mag, I have several revolvers in .44mag, even a desert eagle .44mag (POS), and a half dozen leverguns in .44mag. But if I were limited to ONE handgun and ONE rifle, it absolutely WOULD be a .44mag revolver, and it absolutely WOULD NOT BE a .44mag rifle.
If you honestly can't afford more than one box of ammo per year, then you probably can't afford to go hunting at all and would be better served to save the money for something else.
How much do you really expect to save on ammo cost? A box of premium handgun ammo runs almost a dollar per shot, premium hunting ammo runs about $1.50 per shot (for standard cartridges). For example, I pay $24 for 25rnds of Hornady Leverevolution .44mag for my Ruger SBH, I pay $32 per 20rnds of the same brand for my .45-70 Marlin 1895 levergun.
Say I'm comparing a .357mag Hornday leverevolution hunting ammo with .30-30 Hornady leverevolution ammo: 357mag = $23.99 for 25rnds, .30-30 = $23.99 for 20rnds. That's less than a quarter per round difference. Who cares? If you're high volume shooting, you are going to spend a LOT on ammo, no matter how cheap you can get it.
Even if you're talking about mid-grade ammo that's running $25 for 50rnds of handgun and $20 for 20rnds of rifle, who really saves that much? If you shoot 1,000rnds per year, 500 out of each weapon (about a box per month), you're talking about a difference of $250 (1000rnds of .357mag = $500, 500rnds .357mag and 500rnds of .30-30win = $750, for a difference of $250).
If you're only shooting a few boxes of hunting ammo every year, you're talking about a difference in price of maybe $20-30. But if you ever DO find yourself positioned for a 200yrd shot, or if a mild crosswind makes your shot miss by just a bit on that big buck at 80yrds, that .357mag is going to leave you wishing you had anted up to a real rifle round.