I personally would wait and work on my missions for a bit before purchasing skill books. There are A LOT of skill books in the initial missions and logins, and your roster will look totally different in 30 days, so there might be a number of champs you'll wish you hadn't booked at that point, as you'll be using better champs. 

If you want to get something, get the daily gem pack. And maybe the Forge Pass if you really want to get something else, that could put you ahead on some initial gear farming, although unfortunately there isn't much time left.

And since you asked, some early game tips that can help you:

Your Starter Champion to 60 is your absolute first priority
Using 1, 2 and 3 star champions farmable from campaign, 6 star your starter champion: they are your campaign farmer, and when they are60,they will be able to finish all of campaign, up to Brutal difficulty, for you. They will be farming “food” for you to level up and rank up your other champions. Best spot to farm food is Brutal  12-3. 

It is worth it buying the masteries for your starter, too: it will make it easier for farming scrolls for your other champions too. When they are 50, you can buy the masteries, for 800 gems.  

I would  however  buy the daily gem pack that gives  over 2000 gems  in 1 month . its  under the tab above  limited special offers  in shop called daily & progression

cost me $13 Canadian . Then with all the gems  you get you can fully upgrade your  gem mine and get 14 gem per day forever

you can spend gems on energy/clan keys/shards/masteries/arena tokens and  more. So best deal in the game as far as I am concerned

not worth to spend anything   in this game