Selecting Your Assists
It was only hinted at it in the last section, but there is one more very important aspect of selecting your characters in Marvel Vs. Capcom 3. After picking the character, you are instructed to then select an "Assist Type" for the character. During the game, when you press either Assist 1 or Assist 2, the Assist Character assigned to that button will jump into the screen and perform a canned action. However, what the action is is what is determined by this Assist Type selection. Every character has three Assist Types to be selected from: 
(Alpha Type), 
(Beta Type), and 
(Gamma Type). What the three Assist Types do have been pre-determined by the developers of the game.
However, at the Assist Type selection, all the Assist Types are named and have classifications to help give you an idea of what the action that is performed does. There are two classifications: Style and Direction.
Assist Style
Style, the first form of classification, describes how the Assist behaves. There are three classifications:
This indicates that the Assist Type is a direct attack from the character, meaning they usually will move their entire body to perform the attack. For example, Wolverine's Gamma Assist, the Berserker Barrage, is classified as a direct attack. That is because Wolverine will jump into the screen and charge forward and slash the whole way. Ryu's Beta Assist, the Shoryuken, is also classified as Direct because Ryu jumps up with his entire body to perform his signature uppercut move.
This indicated that the Assist Character typically stays at the back of the screen and fires one or more projectiles across the screen. For example, Doctor Doom's Alpha Assist, the Plasma Beam, is classified as Shot and has Doom come in at the back of the screen and fire his beam across the screen. Arthur's Beta Assist, the Dagger Toss, also is classified as Shot and has him hurl daggers at you from across the screen.
This classification can pretty much be referred to as "Miscellaneous," as they are simply Assists that do not fall into the other categories. For example, Magneto's Gamma Assist, the Magnetic Force Field, is classified as Extra and will have Magneto jump in and activate a counter move that, when struck, will cause Magneto to punish the opponent with a column of magnetic power. Morrigan's Gamma Assist, called the Dark Harmonizer, is classified as Extra because she will come in and just give your team some free Hyper Meter.
Assist Direction
The second form of classification for Assists is Direction. This, obviously, describes the general direction the Assist's attack will be directed. There are 5 directions that are used:
Front attacks are directed straight forward along the ground and are usually used in offense. An example of this is Captain America's Gamma Assist, the Charging Star, where Captain America charges forward on the ground with shield in front to ram into any opponent in his way. Another example is Viewtiful Joe's Alpha Assist, the Voomerang, which is Joe's boomerang projectile that travels forward across the screen. These Assists are usually used for aid in attacking or defense from the front. A lot of these can be used to extend combos on the ground.
These attacks will generally travel diagonally up and forward and usually more defensive based. Super-Skrull, for example, has his Gamma Assist, the Tenderizer, where he repeatedly punches the air at a an angle diagonally in front of him. Another example is Chun-Li's Beta Assist, Tenshokyaku, which has her jump in and rise into the air with a flurry of diagonally upward kicks. These can be easily categorized as the "anti-air" Assists, though anti-air Assists in Marvel Vs. Capcom 3 have very poor invulnerability compared to MvC2, however. Many of them lose out to strong pressure, even from jump-ins, quite easily.
Most Tilt Down Assists attack low to the ground. They are either moves that attack along the ground, like Arthur's Gamma Assist, the Fire Bottle or moves that attack from above, like Amaterasu's Beta Assist, the Cold Shot. Also, though this isn't 100% consistent, but in general, the Tilt Down Assists all have OTG properties for hitting people off the ground for combo extending.
These attacks usually hit right above the character performing the Assist, though it also describes moves that have delayed strikes that can come directly from off the top of the screen to attack. Hulk's Beta Assist, the Gamma Charge (Anti-Air), causes Hulk to charge straight up for example. Doctor Doom's Beta Assist, the Hidden Missile, also is classified with an Upward Direction, and has Doom fire missiles into the sky that rain down on the opponent.
These, once again, can be also called "miscellaneous" as some Assists aren't even really attacks. Amaterasu's Alpha Assist, the Solar Flare for example, is classified as Instant because she just jumps into the screen and puts up a shield that will block and reflect Projectiles. However, while Haggar's Alpha Assist, the Double Lariat, is an attack, it counts as instant because it doesn't really travel in any direction and just attacks in place.
Picking The Right Assist
Thanks to all the varieties of Assist Types, you can really take some time to craft a really strongly functioning team that can cover all the holes in the games of the individuals. If the best Assist for all three of your characters are all classified as Front for their direction, you may consider switching one of the character's Assist so that they are of the Tilt Up type or Tilt Down type for variety and better flexibility. And if all three of your characters use Direct attacks, you would be well pressed to switch one to a Shot type to counter opponent Projectiles.
Strategy Corner
Just as with learning proper roles for your Point Characters, you also need to have a very strong understanding of the possible roles of your Assists to construct the proper team. The biggest mistake you can make in playing Marvel Vs. Capcom 3 is under-utilizing your Assists. If your Assists are not integral to your gameplan, you are either not playing the game right or you have the wrong Assist Type for your character or you may simply just have the wrong character period. As mentioned in the Character Selection section, you can have all sorts of roles for your Point Character: rushdown, keepaway, battery, etc. But it's your job to try and figure out ways to either bolster those abilities or to fix areas of weakness using your Assists.
For example, sometimes rushdown characters like Felicia have problems getting in on keepaway characters if their zoning skills are strong. So you'll need a way to cover your character's approach. A great Assist to use for that would be Iron Man's Alpha Assist: the Unibeam. This fires a beam across the screen and usually beats out most opponent's Projectiles, which is a common keepaway tool. So once you call in Iron Man to perform his Unibeam, you can use that cover yourself and get in closer to the opponent with a Delta Kick or a Rolling Buckler with Felicia.
Another example would be Arthur. Arthur is a great keepaway character from distance, but has trouble keeping opponents away when they get above his head. This is when you may want to strengthen his keepaway game by going with Trish's Beta Assist, the Peekaboo. This move sets a trap in the sky pretty much right above Arthur's head, which works with Arthur even better since Arthur is shorter than most characters. Combining Arthur's great keepaway weapons with Trish's Peekaboo traps can be a very frustrating barrier to get around.
Again, you can also use Assists to cover weaknesses. Some characters need to activate power up moves to be effective, but many of these power ups have delay on activation, leaving you vulnerable to attack. So find an Assist that locks the opponent down for long periods of time to free you up to activate these power ups. Using Amaterasu's Beta Assist, the Cold Star, which shoots a bunch of ice beads and locks the opponent down for a good second or so, you can give yourself opening to activate Morrigan's Astral Vision power up that creates the mirror image of her on the opposite side of the opponent.
Learn how to configure your team properly. It takes a lot of thought and consideration and perhaps the worst thing you could possibly do is to be pig-headed and stick with a team just because you like the characters or because you have a funny team name or something. Yeah, it's great for fun, but if you are interested in achieving 
levels of play, you must be willing to replace members of your team with characters that are better suited to forming a really potent team. Remember, Marvel Vs. Capcom 3 is all about teams, and playing the game with solo characters and never using Assists is the first way to play at a disadvantage right from the start.
There are so many ways to put together a team, so definitely take the time to figure out what assists are the best for your team. And don't be discouraged because it will take exactly that to come up with a good team: time. Be patient and be very willing to experiment.