I used to play this game quite a bit and I started playing it again recently and thought I'd share some of my thoughts and create a standard tier list for you, which I haven't attempted before.
Keep in mind this is merely my opinion and the placements only reflect how they are played and contribute in my Elo (ranking tier), which focuses on large team battles and only in their viability on Summoner's Rift.
Tier 1: Amumu, Morgana, Kog'Maw, Garen, Vladimir, Sona, Taric, Janna, Galio
Tier 2: Annie, Miss Fortune, Twitch, Shen, Ashe, Olaf, Sion, Kassadin, Xin Zhao, Mordekaiser, Warwick, Rammus, Shaco, Kennen, Anivia, Tristana
Tier 3: Nasus, Akali, Katarina, Kayle, Veigar, Nidalee, Pantheon, Udyr, Nunu, Gragas, Singed, Master Yi, Karthus, Zilean, Poppy, Heimerdinger, Twisted Fate, Ezreal, Corki
Tier 4: Blitzcrank, Fiddlesticks, Cho'Gath, Sivir, Soraka, Malphite, Gangplank, Malzahar, Ryze, Urgot, Mundo, Swain
Hard to Place on a Team: Evelynn, Teemo, Jax, Tryndamere, Alistar
Explanation of Tier Groups

Tier 1: Amazing, must-have picks that can be game changing if played properly
Tier 2: Very valuable picks, just below tier 1 that aren't quite as game changing but are fantastic in their respective roles
Tier 3: Good picks that are quite viable but are outshined in their roles by the tier 1 and tier 2 picks.
Tier 4: They are outdone by the heroes above them and generally won't be seen competitively but can be added fill in certain gaps in the team composition and are not completely inviable.
Hard to place on a team: They aren't as good as the other heroes in their respective roles and aren't competitively picked. Bottom of the barrel.
Bad items: Malady - (Completely outshined by Starks Fervor and the passive is worthless)Warmogs - (Health Regen is not a good stat outside the early laning phase, most fights are over in a few seconds. Health is a good stat but its the only thing warmogs provides and is grossly ineffecient in terms of health per gold, until you fill the thing full. However you're losing out too much in other stats if you make this investment)Philosopher's Stone - (Regens, again. Inefficient item and the gold tick is basically worthless; unless you're getting it for Shurelya's then its not worth the investment)Hextech Revolver - (Spell vamp is not worth the gold)
Tiamat - (Too much gold wasted on regens, the passive is cool but you aren't likely to get much out of it and if you're supposed to be dps you've got other items you need far more urgently)Phantom Dancer - (This item isn't actually bad, but its very expensive and you're spending much of it on two stats you might not need (movement speed and dodge). In general it isn't a good idea to invest this much time in attack speed and it shouldn't be gotten before your first high damage item (IE infinity edge). Dodge also has diminishing returns)Wit's End - (Completely outdone by other damage items. The passive deals magic damage, so it doesn't gain from your armor penetration and can't benefit from crit. Can't hurt people who don't have mana. Your attack speed should be acquired elsewhere)Good items:Aegis of the Legion - (Good survivability item with only stats you might want and basically hands 730.02 gold worth of stats to each of your teammates)Randuins Omen -(Amazing active and a piss ton of armor and some health. Most physical carries will have enough armor penetration between brutalizer/youmuus and runes to take you from your standard 30 armor to 0. Add in a randuins and you've halved their attack damage right there, not including the aoe movement and attack speed slow. Only need one per team so usually best left to tanks. Built from heart of gold which is fast hp/armor before you ever need to finish item)Stark's Fervor - (Gives AS to all your teammates, -armor to all your enemies. Great item, good for your Attack Speed item (which you usually only need one of))Guinsoo's Rageblade - (Good for hybrid builds. At max stacks it is disgustingly efficient (3995 gold worth of stats for its 2235 gold price))All the Dorans - (Efficient items with early hp and regen you need to stay in the lane and the stat of choice. Can be sold later. Stacking a couple dorans blades early on for on physical attack carries is common in high tier gaming)Madred's Bloodrazor - (Built from Madred's razor which is an excellent jungling item. Since it deals a percent of their max hp in damage you might think its just an anti tank item, but the item breaks even in damage when the target has ~800+ hp, which they are certain to have. Good passive, and all stats you want as a carry (armor, flat damage, attack speed))Banshee's Veil - (This item is awesome. Magic resist is hard to come by, compared to armor (there are 3 items that give 100 armor, highest MR you can get is 78 on the inefficient Force of Nature) and gives good health at the same time. This item is gold efficient in stats alone, plus its passive which is amazing. This item is good on every champion (less so if you don't have mana) as you should always incorporate survivability into your build, no matter your role. If the enemy team is magic heavy and you've got the items to fulfill your role, get one of these)Bloodthirster and
Infinitely edge - (Both excellent damage items, highly recommended)Rod of Ages, Archangel's Staff, Rylai's Crystal Scepter, Lichbane, Zhonyas Ring - (All great mage items)General tips:
- The goldilock zone for tanking is ~3000 hp and as much armor/mr as you can get in proper ratio to the enemy's damage output types. Try to get armor/mr to ~300.
- Having someone jungle is important (not
always needed though), since you control the red/blue buffs, can get dragon kills (which give 130 gold and exp to everyone) and can gank each lane when needed. Since they don't know where you are, enemies have to play cautiously if they don't want to get ganked)
- Buy wards! Map awareness is so so important. If I'm playing a tank or support I may buy as many as 6-7 wards in your standard game.
- Damage > Attack speed. Theres no point in attacking fast if you don't do any damage and you can't guarantee many successive hits. Usually you only need one attack speed item if you're an AD (attack damage) carry.
- Revive is always a bad summoner spell. It only benefits you when you're dead and can only be used every 9 minutes.
- Heal is not that good of a summoner spell. If you aren't a tank, the added health isn't going to have that much weight. In general you can subvert more incoming damage with ghost or flash. Your heal isn't going to matter if you can't outrun that Olaf that has ghost up. Ghost and flash can be used offensively too, whereas heal cannot.
- Don't over push your lane if they have a jungler. Keep tabs on everyone on the map and call out 'mia' if the enemies in your lane are 'missing in action' (noobs stuff, I know)
As for the game I played with Devlin/Echo/Zycorax/Artanis, I was disappointed in my own performance because I kept missing key Shen Ult saves by a millisecond. I logged off to switch to a lowbie account (pumpkin pasty) to queue with you guys so that I didn't influence our Elo too much. But I found out I had to go.
None.