First off you have to check the Colorado hunting regulations to make sure the rifle is powerful enough. There may be a minimum power requirement for rifles. I've hunted deer in South Dakota, and there the minimum muzzle energy is 1,000 foot-pounds of energy. The .44-40 only makes about 625 ft-lbs in a rifle. Some states may have a minimum bullet size as well, such a .243 caliber, or require expanding (hollow point or soft-nosed) bullets be used.
If you already have the .44-40 and it is legal for deer, then you simply have to either shoot from the standing or kneeling positions, which as close range is not a problem, especially if you can brace the foregrip (not the barrel!) of a rifle against a tree limb or trunk. For sights, you might want to see about TruGlo iron sights. These are fiber-optic sights that gather up ambient light and concentrate it into a point of green or red that is easily visible. Of course, the red-dot sights would work quite well, but the TruGlo sights are probably cheaper and don't require a battery.
http://www.truglo.com/content/prod_long_gun_sights/Slug%20Gun%20Sights.aspConventional wisdom is that deer can't see red light; their visual detection spectrum does not go as far down as ours does. So the laser projector actually is not a bad idea as long as the hunting regs allow for it. If you're not sure, give the Game, Fish & Parks a call. If you can use it, practice with it!
If you have not bought a gun yet, you might want to look at a bolt-action rifle from Remington or Savage. They make "youth" models, which have shorter stocks and barrels for people of short stature. I have noticed that your profile says you are fairly short, so I am trying to work within that parameter. My ex was a mere 5'0", so I can understand.
There youth models are usually what are termed "short action", which is a cartridge as short or shorter than the .308 Winchester. The Savage Model 11FYCAK (
http://www.savagearms.com/11FYCAK.htm) comes in .243 Winchester, 7mm-08 Remington, and .308 Winchester. My ex-brother-in-law has a bolt-action Savage in .270 Winchester, and it was a fine rifle, easy to load, easy to work the bolt, and easy to shoot. And new Savages have the Accu-Trigger, which makes the trigger pull lighter without compromising safety.
Remington makes the Model Seven bolt-action, which is sized to fit small-statured people. Remington coems in the same calibers as the Savage plus a few more. It is available in the fairly new 6.8mm SPC (.277 caliber), which has a muzzle energy of about 1800 ft-lbs and good on deer to about 200 yards or so.
http://www.remington.com/products/firearms/centerfire_rifles/model_seven/model_seven_CDL_specs.aspThe .243 Win is generally considered adequate for deer up to about 300 yards with a good bullet, assuming you can shoot accurately at that distance. It makes about 2,000 ft-lbs at the muzzle, which isn't all that much when fired from a shoulder-fired arm.
The 7mm-08 (.284 caliber) is good for deer up to about 450 yards with a good bullet, and makes about 2,400 foot-pounds at the muzzle.
The .308 Win the the same round used by the military in machine guns and military rifles. With a good hunting bullet they are powerful enough for deer past 500 yards, and makes about 2600 ft-lbs at the muzzle.
Savage also makes regular-size rifles in .223 Remington, which is very popular and cheap because it is what the Army uses in the M16s. It is usually used for varmit hunting, like coyotes and groundhogs, and for target shooting, but you can get hollowpoint "match" bullets or Nosler Partition bullets that would be good for deer. The .223 makes about 1,300 ft-lbs at the muzzle, and should be used on deer within a hundred yards.
If you want to get an autoloading rifle, you can get a Ruger Deerfield Carbine 99/44, which is chambered for the .44 Magnum. A .44 Magnum fired from a rifle makes about 1600 ft-lbs.
Ruger also makes the Mini-14, which in an autoloading rifle in .223 Rem, and the Mini-30, which is the same rifle chambered in 7.62 Russian. The Mini-30 fired the same .30-caliber bullet as the AK-47, so practice ammo is very cheap and deer ammo is readily available. The 7.62 Russian makes about 1600 ft-lbs of energy and would be good on deer out to about 150 yards.
You can also get a number of good-quality AR-style rifles for the same money as a Mini-14, and they tend to be more accurate than the Ruger and most of them are made to take scope and sights and such. But they are military-looking and turn some people off, even though functionally they are exactly the same as the Mini-14.
I've personally fired a .223 Rem and a 7.62 Russian AK-47, and the recoil is pretty light.
You can also get a more-powerful lever-action rifle if you like the lever action. A .30-30 is about as powerful as the 7.62mm Russian, and you can get them from Marlin and Winchester. You can also get them in .44 Magnum, .357 Magnum (about 1200 ft-lbs), and .45-70 (about 2400 ft-lbs). Marlin's rifles are also drilled and tapped for scopes, and you can buy a Marlin-made rail to extent the scope mounting surface further towards the muzzle so you can put on a "scout" scope, like the other poster showed you.
http://www.marlinfirearms.com/Firearms/Centerfire/336A.aspxJust please note that the Winchester factory in Connecticut has closed down, meaning that they are no longer making bolt-action rifles, lever-action rifles, or pump-action shotguns. I'd go with a Marlin.
http://www.winchesterguns.com/prodinfo/features/detail.asp?ID=116Hope this helps you out! :-)