The game is flexible enough that you rarely have to worry about having someone in your team, so feel free to pick whichever characters you like. The same goes for the number of units you'll actively be using (you can have 10+ characters relatively at the same level or 1~2 op characters/dmg dealers if you want). Though I've never used them, the characters you get from the summoning experiments are pretty good overall (also, bear in mind that the lv of the chars you get from these events are based on the chapter you're on, but the devs forgot to adjust the prizes from the bonus list, so you probably have more money/EXP and more powerful items than you should've at this point).

With that said, a few general tips (not limited to team building):
- It might come in handy to have one or more characters that can use Fist skills (like Adell) for moving enemies in the item world (a well known mechanic in Disgaea games that you'll be introduced to soon-ish).
- Similarly, having some spare characters in reserve with a good throwing stat can help a lot with moving your main characters. Early on, I usually create a bunch of beastmasters (you need to unlock the class first by passing a bill after capturing an enemy), but the basic warrior class can be used as well (beastmasters have a few more utilities other than just throwing people around, but it probably won't be relevant to you).
- While this might be a little biased, try to pass the bill to unlock shoes for the shop ASAP. Movement is a pretty important stat throughout the game.
- It would also be prudent to check character's passive abilities and, to a lesser extent, their skill set to make the most of it. Rozalin can buff male characters just by standing next to them, Prinnies can be used as portable bombs, Rifle Demons (which will take a while to unlock) can't miss their attacks etc. While not strictly mentioned in-game, Thieves have skills that inflict status effects 100% of the time (excluding marionette enemies (due to their own passive) and bosses), which is pretty abusable. Later on you unlock the Kunoichi class which have an AoE version of most of these status skills, and while it's not a 100% infliction rate, it's still pretty accurate.
- In general, magic > physical attacks. While you shouldn't completely neglect physical skills, magic in this game has a few more benefits compared to physical skills, especially for humanoid casters (power, range and flexibility). I'm not saying that the physical side is weak or not viable (not to mention having some versatility, like what I've said about Fist skills), later on it'll simply be a matter of overkilling enemies or completely erradicating every trace of their existence.
- With that said, you might want to learn a bit about inheriting spells for your characters (especially for the "mage" characters you got from the summoning experiments, since they don't learn regular spells on their own). The gist of it is that you create a character that naturally learns magic (usually Mages/Skulls and/or Healers, that will be the "Student" or "Pupil") with a character you want to learn it (a "Master"). During battle, have both of them stand side by side. The "Master" will have available the spells the "Student" has to be cast, starting at lv 0 in skill mastery. If the master cast it repeatedly until the spell gets to lv 1+ (usually 4~5 castings), you don't need to have the master stand next to their pupil/student for further use. Do know that you can't learn every type of spell, only the "generic" ones - fire, wind, ice, star, heal, espoir and their upgrades) and buffs/debuffs (again, only the generic ones from healers and mages/skulls).

Very helpful thank you! This game seems have quite a bit of a learning curve but this has simplified it quite a bit

Disgaea (unlike most rpg´s) doesn´t punish you for having a "bad" party or forces you to take a certain way. But ....
a) As mentioned above , I don´t use too many of the special Chars too. They are overpowered and take away the fun of developing classes to higher skill levels.
b) I try to resist the temptation of relying too much on Mages . You will detect soon how comfortable it is bombing everything away with Area Mega Fire, Ice etc
C) Usually, just for the sake of gameplay, I don´t visit the Item World on my first Run. Too many Item Wolrd visits quick lead into a boring cakewalk in the main story. And yes , you lose a bit time going undeveloped through the main story. But who cares in the end how much playing time I need.

Aside from Adell, Rozalin, and the other storyline Humanoids, I highly recommend:
-At least 2 units besides Adell that use Fists for manipulating enemy positions (especially in the Item World)
-A Bow user (preferably an Archer)
-A Thief with either a Gun or a Bow
-A Heavy Knight to help with throwing with a Spear for personal mobility
-Three magic users (start with one of each element Skull to help with learning spells faster, then Reincarnate one as a Star Skull, one as a Healer, and the third as a Magic Knight)
-A Ninja with Fist and Sword experience and a Felynn student (Fist equipped for Team Attacks and Sword experience for Magichange with the Felynn)
-Have Tink make a Beastmaster with an Axe, a Succubus, and a Flora Beast (Tink's red form pairs quite well with them for Team Attacks, his passive stat boost for being adjacent to Females, and the Beastmaster's passive to boost adjacent Monsters)

Any characters are good and you can solo the game with anything.

Party composition isn't required for anything, but it can make the game easier.

Making sure you have basics like Healers helps a ton. Keeping a Mage on tap for their long range or for busting enemies with high physical defense or resist is a good idea.

Some Disgaea games let you get bonus stats for having certain team compositions, like Beast Tamers giving/getting bonuses to/from monster demons.

But it's not often you can do any serious team composition builds, like having tanks and healers like you would in other RPGs... since movement is not very restricted and so many units have extreme ranges, it's hard to actually block off your enemies in such a way that they will focus tanks rather than your squishier units.

You also don't have to have any squishy units since... any unit can use any gear. So Mages don't just have to be Glass Cannons, they can also be impossible to kill with high defense scores.

So in short: There is no way you really should structure your team. Just have fun.