Team building help/suggestions.

Team building typically revolves around optimizing usage of card types and skill. For example, the most basic team type is the buster chain spam team typically involving berserkers. This requires all members of the team to have at least 3 buster cards (can include np) and as the name implies, simply spamming buster attacks. Usually the team people transition into is one of the various arts teams. Arts teams revolve around the same concept of chaining arts cards so that the servants can use their NPs more often. Typically this involves two combos: dps, support, support or crit dps, support, star gen dps. A dps is the designation given to the main and strongest attacker in the group. A support is the designation given to the one that buffs others the best with skills. And a star gen is a servant that manages to generate critical stars in decent amounts with attacks.
The soon to be strongest team archetype is the buster crit team. This typically involves having a star gen generate a bunch of stars and throwing all buffs including buffs to critical damage onto one dps that can and probably will collect all those stars due to having a high star absorption rate. Typically these are riders and archers. Merlin, who will be out soon, makes these teams what they are by providing them all these buffs removing the need for a star gen or secondary support.
Lastly, there's the quick crit teams that as the name implies rely on chaining quick cards so that they can always be generating stars and critting with those stars. The quick crit team is currently a little bit away from being fully viable however because their best support is at least 2 years away from being available.

There are multiple variations on these team types based on servant abilities and how they synergize. I do encourage you to look into the strengths and weaknesses of your respective servants as they are a great way to learn about their uses. A good website to do that is in fact right here. My suggestion however is to not worry about building teams beyond basic team concepts of applying as much class advantage as possible until you have at least 1 max levelled servant in each class (other than ruler and avenger). If you want to know who is ideal to use and why to use them, consult the tier lists here and then read the servant pages on how best to use them. Hope this was helpful

For now just max out your servants and use class advantage. Once you have done so, you can try a couple things.
1. Waver, mash, helena, and hans are sort of universal supports in that they fit in any team comp and do well.
2. Pick another from above or use chevalier for tanking, medea lily for healing, or saint martha for buff/debuff clears.
3. Choose a damage. Altera can hit hard. Chloe does a lot. Nobu for divine/riding enemies. Emiya will be good once last sq comes out. Santa alter or ushiwakamaru. Anne Mary is difficult to use, requiring specific CEs and team comp. Shiki for most teams, carmilla vs females. Medea for np spam. Heracles for raw power. You lack a good offensive lancer. Try for the babylonia pickup summon. However, it is not limited so you might want to raise cu proto and wait for christmas.
4. Fill with any servant you need/like.
5. Cu fsn for backline.
You can go support damage damage instead, but your servants might die quicker.