You can play any way you want to and do not have to jungle. However, some champs are so good at jungling, that one usually prefers that to normal laning (Amumu, Shaco, Skarner and the like).
You are right, that a jungler means that one other player is left alone against two enemies. However, he has the protection of a turret, which is enough in the early game to survive. Plus, he levels almost twice as fast as his two enemies, so he will very soon have his ultimate available against two level 3 or 4 enemies. Of course, some champions have a hard time to stay alone in a side-lane. Make sure when you have a jungler in your team, that you have a solo-champ that can hold its own without problems.
Jungling can only theoretically be done by all champions (sure, anyone can go into the jungle and attack creeps there). However, most champions are way too slow to make it worthwhile. They would profit much more from staying in a lane. These champions should not try jungling. If you want to try jungling yourself, then select a champion, for which you have one of these jungling guides at hand. Don't just try any random champion out in the jungle.
Finally, the most important point about jungling is one that most novice players often forget. You do not jungle in order to remain in peace and level up on your own. You jungle, so you can level up and at the right moment appear in a lane for a surprise gank. Enemies have to be constantly aware that a jungler may pop out of a nearby brush all of a sudden turning their 1v1 or 2v2 lane into a 2v1 or 3v2 problem. If done right, jungling can very quickly devastate your enemies, because the jungler has the power to turn around any lane. If one of your team's lanes is having trouble, adding another champion to it will devastate the enemies and at least break their attacks. Often, you can even net a kill or two. If you're a good jungler and help out frequently with ganks, then you will soon outlevel your enemies and the game can be pretty much decided in less than 20min.
So in summary, do not doubt jungling. It is a very popular and strong strategy. However, be aware that being a good jungler is not easy. Especially, when playing together with other novices, who may not know how to deal with a jungler in their own team. I suggest, you try to get at least several dozen games of normal lane-gameplay done, before you try out jungling yourself. And then, start with practice games, so you are certain, that you will survive the early jungle farming. It is most embarassing to die to the golem when no enemy was ever present.
I would recommend you to get tier 1 runes until you get to summoner level 20, then as akaGrim stated, you can get the Tier 3 Runes.
These are general purpose (In the sense that they can fit any champion) tier 1 runes that will aid your way to level 30 and they are very cheap:
3 × 
Lesser Quintessence of Fortitude +14.6 Health (165IP each - 495IP for the set)
9 × 
Lesser Mark of Insight +0.53 Magic Penetration (30IP each - 270IP for the set)
or
9 × 
Lesser Mark of Desolation +0.93 Armor Penetration (30IP each - 270IP for the set)
9 × 
Lesser Seal of Clarity +0.036 mana regen / 5 sec. per level (+0.65 at champion level 18) (15IP each - 135IP for the set)
or
9 × Lesser Seal of Vitality +0.72 health per level (+12.96 at champion level 18) (30IP each - 270IP for the set)
or
9 × 
Lesser Seal of Shielding +0.05 magic resist per level (+0.9 at champion level 18) (30IP each - 270IP for the set)
or
A combination of the above mentioned
9 × 
Lesser Glyph of Focus -0.36% cooldowns (65IP each - 585IP for the set)
or
9 × 
Lesser Glyph of Shielding +0.08 magic resist per level (+1.44 at champion level 18) (15IP each - 135IP for the set)
or
A combination of the above mentioned
A total set of runes will cost you around 1620IP, It is quite a bit but it is worth getting, it makes a difference on early game.
Assuming you will play with a 50/50 win/loose ratio you can get your complete set of tier 1 runes in less than 30 matches.
There are also many recommended champs for beginners which are usually very IP cheap, I am talking about champions like:
Ashe, very easy to play Attack Damage Carry, 450IP
Ryze, easy/medium skill Mage, fun to play and very powerful! 450IP
Nunu, easy/medium skill Ability Power 'Tank' 450IP
There are many other cheap champions in the price range of 450-1350IP, don't hesitate to buy one if you are liking its playstyle, as you may have noticed Riot rotates the free champions every week and you might want to play a champion you liked from the previous free week on the actual.
For more information on runes and recommended champions check:
League of Legends Learning Center: Champions
League of Legends Learning Center: Runes
Best Answer
Map Awareness
Riot has garnered some pretty effective videos with their Video Tutorial contest (Links posted below). As a beginner, you want to primarily focus on making sure you don't get ambushed by the other team (called a "gank"). While some of this involves Map Awareness, you also need to learn to not overextend, as well as keeping an eye on the enemies you're fighting in your lane. If you cannot see one or both of the enemies in your lane, let your teammates know!
Last Hitting
Killing minions and enemy players nets you gold to buy items. However, if you don't land the killing blow on an enemy minion, you will get ZERO gold, even if you've done most of the damage to it.
The faster you kill enemy minions, the faster the minions reach the enemy tower, which will make quick work of all non-cannon minions. It's better to keep the minion fights as close to the middle as you can; you only need to finish off the minion to get gold from it -- see if you can limit yourself to only attacking minions when you will kill them!
Tower Aggro
The enemy towers are dangerous. They have lots of health, armor, and a powerful attack that can quickly decimate low-level heroes. It's important, then, to know how the turret picks its target.
Enemy towers will always target allied minions first, switching to champions only if there are no longer any allied minions around. The exception to this is if you deal damage to an enemy champion, in which case the tower will immediately switch to the damaging champion, shooting at them until they die or move out of range.
Let me repeat that: If you deal damage to an enemy champion within range of the tower, it will immediately start shooting at you: You do not want this. Be very careful when attacking the enemy at their own tower.
Recommended Viewing
Four of these videos are a result of the Valoran Video Contest held by Riot Games, and are quick, 1-minute videos touching on just the basics (which seems exactly what you're looking for). The fifth video is made by Shurelia, an employee of Riot Games, and goes much more in-depth into what "Zoning" is, and how to take advantage of it.