It's been a while since the initial release, but I do remember there being a bunch of obstacles for newcomers.
You're probably going to be very limited in QP (currency used for level ups/skill ups/etc), and xp cards will also be low in number. Do not try and level every Servant you get, focus on a specific party. Whatever golds you have + any good bronze/silver Servants are the ones to look out for. Shielder (your first Servant) isn't completely amazing at first, but she's still worth carrying around. Just don't expect her to carry the team for you.
Don't level skills at all at the beginning. They're late game progression and you'll run out of QP and materials fast if you do it early.
This is a good list indicating the overall power level of the launch Servants. Since you won't have a full team of golds, pay attention to the bronze/silver and consider using them in your party. Don't bother using crappy ones (unless you like them). I think during JP release I mostly focused on F/SN Lancer, Kiyohime (yandere berserker) and F/SN Assassin. They carried me through the early game as I had literally no golds.
- - - Updated - - -
Also, it might be tempting to level a Servant of each class at the beginning, but you really shouldn't. You won't have the xp to spare. Like I said, for the most part focus on a specific party. You can fill in holes in your team by using other people's Servants with the support system.
(Saber Lily is also mostly useless, might not be a good idea to use her)