Yes, the 7.62x39 is an effective deer killer up to distances of 200yds in the hands of someone who knows how to shoot it. Here's a few observations of mine:
Even the sloppiest examples of Chinese SKS will group within 4-5inches at 100yds, often considerably less for better specimens. With a bit of practice (possible with the relatively cheap cost of ammunition) an SKS owner could effectively hit an area the size of a deers vitals at 200yds. Some people have reported being able to consistently hit gongs at 300yds, though at that distance an SKS would have nominal stopping power for deer sized game even if you could shoot that well.
By stopping power, I am considering 900 foot/pounds the minimal for hunting deer, which is met by the 7.62x39 up to 200yds. While the 30/30 has higher muzzle energy, the SKS shoots flatter beyond about 150yds while the difference in killing power narrows as well. While a .223 also has the same energy at 100yds, the smaller bullets used by that calibre have problems penetrating and holding together on deer-sized game, making such a shot undesirable in all but survival scenarios. That issue has been covered to death in other threads.
If you are new to shooting and want a first deer rifle, an SKS is not a bad choice. Even if you buy a more expensive rifle in the future, you will certainly continue shooting it for fun, and could bring it along as a back up rifle for bad weather or in the case that your primary gun fails.
If price is an issue, sporterized examples of the .303 Enfield could also be purchased at a similar price to the SKS, though cheap surplus ammo for practicing is a thing of the past. The Enfield would have added killing power for deer, bear and even Moose within reasonable ranges. Another option would be one of the Mosin Nagant Rifles. More expensive, but relatively cheap surplus ammo is still available for them, and the 7.62x54 also has greater stopping power more within the range of a .303 or .308 rifle.
The Stevens 200 is a great deal (I have one in .223), but at around $350 delivered to your door, plus the $125 for a scope, you'll be spending close to $500. An Mosin or SKS with 450-1000 rounds of surplus ammo can be had for considerably less money. If you live in a prarie region of the country where long shots are fairly common, I'd spend a bit more for a Stevens in a calibre like .308. If you live in a region like Ontario where shots are rarely beyond 100yds get a 7.62x39, or a slighty heavier .303 or .308 if you think that you'll try for bear, moose, or hunt be hunting in really thick brush where a heavier bullet might be of help.
Best of luck with whatever you choose!
Frank