Herc is definitely really good and probably the "best" Servant you can get through that tutorial/starter roll. Waver is probably the best Servant you can get with the Free SSR after Fuyuki, yeah. I would probably use the Special Ascension on Waver of the two.
It's not so much that mats for 5* Servants are harder to get, they just tend to use more of them than the lower rarities. However, there's a shop in the game where you can buy up to 100 of any material using a currency you gain for advancing the main story. You don't end up with
much
of that currency even once you're up to date on the story, but it's a decent "break glass if emergency" option.
As for getting through the story - you can probably power through most of Arc 1 by just grabbing OP Friend Supports and having them carry you. If you pick Waver as your Free SSR he can even help support them. Some of the better Servants for just speeding through the story would be strong Berserkers like Arjuna Alter, Morgan, or Summer Musashi. As well as just broken Servants like Melusine and Space Ishtar. Aside from sending Friend Requests as a new player you can also choose to follow a few (3? IDK by the time they added it I was too far to use it) players which allows you to use their Servants' Noble Phantasms without needing them to accept your friend request for Arc 1. So I'd look for people who have those Servants - ideally at a high NP level and maybe consider following them to use those Servants to just trivialize most battles.
May you find your book in this place.
Formerly known as xp1337.