A guide to effective murder machine creation, borrowed from the impeccable C. Steven Ross:
Level 1
FTDM starts and ends at first level, that's it. No magic items ('cept what's in the maps). No paths or destinies. No feat combos ('cept for humans, and that's only two). No stat bumps, no utility powers, no retraining. Many of the CharOp boards' builds go to level 30 and essentially disregard first level. Even with the limited resources available, there are still billions of possible permutations, and millions of them are going to be kickass.
tl;dr - 30th level super-builds won't help you here
Encounter Powers
Encounter powers are your bread and butter. You die and respawn A LOT. If you die every round, you get fresh encounter powers every round. Essentials builds tend toward encounter boosters, without a daily bang. Since they're balanced against AEDU builds, this can sometimes trend towards unbalanced (read: better!) in FTDM. Also, if you only last a turn or two? Standard action encounter abilities are less interesting than ones that take less time. For example, multiclass striker feats that boost damage "once per encounter" have a pretty good bang for their buck in FTDM.
tl;dr - treat encounters almost like at-wills
Daily Powers
Daily powers with "end of encounter" effects are bomb. I've seen players "waste" the attack/damage of their Daily just to get the effect. Even if there's a sustain effect, take a good look at it. Remember, you can sustain through respawn! (but not stunned) Resistance? Defense boosts? Phantom Chasm? Damage boosts? All gold.
tl;dr - if your daily doesn't have an EoE effect, it had better be sweet
At-Will Powers
The little I will say here is that unless you have some stupid-awesome combo, humans and half-elves take their Essentials racial powers.
Hybrids
Full leaders are generally unnecessary. A pretty consistent design I've seen is the hybrid leader with an emphasis on another role. One heal per "encounter" is generally plenty. Also, a lot of the roleplaying "fluff" and higher level awesome that gets chopped off of hybrid characters (which is why people avoid them) doesn't matter much in FTDM.
tl;dr - hybrids? better than you think
Defenses
Killing one guy with one low defense three times is easier than killing three guys with high defenses once each. This goes both ways, and is probably directly responsible for WetwORCs losing the very first PbP match, despite good builds and tactics. Good strategies are having options to target multiple NADs, and accepting that your 11 in Fort or Will is going to be a big red circle.
tl;dr - shore up your defenses, or expect your bad NAD to get you killed
Hit Points
The current errata outlaws weird backgrounds (Auspicious Birth and other HP-swaps) which would be gold, so a Con-centered build will help with HP. FTDM doesn't have a healing surge economy, so starting HP is what you rely on. The most effective all-around FTDM builds combine high hit points with high damage - you want to be able to nova and one-shot other dungeoneers, but be able to survive your opponents' novas.
tl;dr - high hit points, high damage
Race
The simple answer in this case is to find powers that directly contribute to the two prime directives of FTDM: don't die, and kill fast. For example, the gnome's Trickster traits and Fade Away pale in comparison to the half-orc's Resilience and Furious Assault, at least in FTDM. In terms of ability bonuses and racial feats, peruse the CharOp boards. Most races have obvious (and hidden) killer combos for FTDM.
tl;dr - support your focus, follow CharOp
Skills
Even hybrids with their tiny skill list will do well here. Unless a map has features to make skills useful, the only good ones in FTDM are Athletics/Acrobatics and Perception/Stealth. This is in direct opposition to the way most Fourthcore adventures (and even regular D&D) operate. There aren't skill challenges. You aren't making monster knowledge rolls. You need to jump pits, break your fall, notice invisible people, or be unseen. A background to get one of the core four as a class skill isn't a bad idea. Some maps have special effects if you're trained in a skill- so don't discount the extras.
tl;dr - Athletics/Acrobatics/Perception/Stealth - go!
Map Optimization
This is going to have its own Boot Camp at some point. As you've probably noticed, each of the maps can have wildly different strategies. Terrain hazards? (E1M1, E1M2, E4M1, E5M2) Use and defend against forced movement! Tight hallways? (E3M1, E5M1) Wall of fur, teleports, shift through people. In E4M1 the big terrain power causes permanent blindness. Building for that, you could fully expect to be blind half the match, and prepare bursts, blasts, and blind-fighting. I haven't seen it in play yet, but E5M1 will probably favor speed and snipers. E2M1's tiny platform can be dominated with encounter-long zones. I honestly don't know what to think of E6M1 - it's too freakin' random to plan against.
tl;dr - understand and prepare for your map
Glossary
FTDM - Fourthcore Team Deathmatch
tl;dr - Too long, didn't read (basically, the section summary)
CharOp - Character Optimization, the science of getting extreme results from the system
Nova - expend several resources to do a ton of damage
One-shot - damage an opponent enough to bring them from full HP to 0 or less in one round
AEDU - short for at-will/encounter/daily/utility - Essentials scrapped this design to make more individualized classes.
Gold - the color coding system on the CharOp forums uses gold as "must-have"
NADs - Fortitude, Reflex, and Will, or the "non-AC defenses"
Wall of Fur - a fringe build that relies on multiple beast companions or summons to provide roadblocks, flanking, etc.