Team composition for a newbie, please ?

Ok first off what servant of each class to invest in?

Saber- The only gold saber you have and even if you get another gold saber if its not a 5 star the star difference will be pretty large, so you can still use her even then.

Archer- Robin hood is probably the best archer you can invest in right now and possibly euyrale later, also invest in david for his support he can offer.

Lancer- Karna is best aoe lancer in the game and has a lot of utility with his kit, a np seal, mana burst, and a np battery skill.

Rider- Saint martha would be good for farming and has a good kit, but if you want a rider for boss fights and such I would go for ushi who you can get from fp gacha.

Caster- I would go for hans first since casters in this game aren't the best at attacking since they have .90 damage modifier and usually the support other casters can bring is a lot better. Go for hans first than go for da vinci for farming.

Assassin- This one is pretty simple go for Jack first and I don't really see another one to invest in since jack is the best assassin in the game for the far future.

Berserker- You have raiko who can be both a farmer and a crit damage dealer, so yeah go for her first and than Hercules you don't even have to level up herc just work on getting his bond up since he becomes 5 star level with it.

As for other servants such as ruler and shielder, you really don't have to pick which one to level since they're so rare that you should finish leveling one before you get another unless you have ex luck.

As for teams comps, I won't spend as much time on this since you didn't specify a arts/quick/buster team setup, so i'll just use the best team that work in most circumstances "buster crit".
You already have 2 servants that work great together and all you need to round it out is a support waver. Jack(Crit star generator)/Raikou(Main damage dealer)/Waver(Will help with np gen and also provides good buffs for the party). Since raikou is a berserker she will steam roll most of the game since she will deal 1.5 damage to every class for a long time. For backline just survivors or other buster servants to hopefully kill them before they kill you.

If you are still progressing in the story, Mash, George, Minamoto, and a good support will complete all the current content we have, Mash/George being the most important as they can protect the support your using, which is basically all you need at the moment. Outside of that you will most likely want to increase your farming servants first as it speeds up leveling everyone else. Minamoto No Raiko and Kiyohime are AoE berserkers so they can be used to farm anything; Karna, Altria, Medusa, and somewhat Elizabeth also do the job well as long as they are not with class disadvantage. Rider Kintoki and Jack provide excellent team choices for harder content so those are good choices for when you have need of large amounts of critical stars.