How many character slots do you get

No it's not. You should also put points into the secondary skill tree at least to the point you get a good consumer ability.

The reason this is better is because most builder abilities are building up point for both weapons you wield. This way you will be able to double the output of consumer abilities and this will increase your damage (or heal) output at least by 15%.

• builder ability: Abilities that build up points for your weapon (up to a maximum of 5).
• consumer ability: Abilities that spend these points and usual do more damage/heal than builder abilities.

Other source:

Why do I need two weapons? What's wrong with just one?

The game is balanced around the type of damage output you can do with one builder ability to create 5 resources for two different weapons, followed by using consumer abilities from each weapon back-to-back, and then repeating this general process. If you have only one weapon, then you have only one build cycle followed by one consumer, and you are essentially putting out only 60-70% of the total DPS that you could do if you were using two weapons.

So don't try to skill up only one weapon to "max" Skill 10 ASAP, because you're seriously gimping yourself by doing so. Right from the start, as soon as you roll into the Sheriff's office in Kingsmouth for the first time, you will receive your choice of a second weapon, and you should always roll with two weapons at all times. Three of your active abilities in any 7/7 build should always be: A) some type of builder that will build for both weapons with each hit, B) A hard-hitting consumer for Weapon 1, and C) a hard-hitting consumer for Weapon 2.

Source: http://yokaiblog.wikidot.com/guides:tswfaq

Log in to your character, open the in-game shop (!) (default key ".") and then use the first menu entry on the left. There they are, your items - you can now "buy" them for 0 points. After buying, they appear in your inventory.

You can do this once per character, I'm told.