Choosing Your Alpha Ability
The Alpha slot can hold one of four types of specialized Enhancements--no ordinary Single-Origin, Dual-Origin, or Invented Enhancements will do!
What you'll need to do, before you choose what type of specialized Enhancement to slot, is decide: "What needs boosting on my character?" For instance, if I wanted to boost my Recharge Times of all my powers, as well as Healing, Jump, Slow, To-Hit Buff, and Stun Duration, I'd reach for a Spiritual Alpha boost. But, if I wanted to boost my Damage, as well as my Immobilization, Running, Defense Debuff, To-Hit Debuff, and Endurance Modification, I'd reach for a Musculature Alpha boost, and so on.
This decision is completely yours--there's no "right" or "wrong" way to build your character at this point, and you can customize it for the way you play. Some people will want more damage all the way, while some would prefer to increase their recharge times, and some will need accuracy boosted, etc. (You can bet I'm boosting Lyssadia's Accuracy as high as it'll go when she finally hits 50--I'm tired of shooting pretty Energy Blasts at the ceiling! On the other hand, I'll definitely want to boost Wubbius' Endurance, since Grandma needs a little bit more energy these days.)
Learn about the four basic types of Alpha Slot enhancement on the ParagonWiki Alpha Slot Abilities page.
How Do I Get to These "Levels?"
Levels of the ability trees are attained by building rarer and rarer versions of the Enhancement. A simple Common Spiritual Enhancement, for instance, will get you a 33% boost in all your powers that can take a Recharge boost. (Remember, you have to build these Enhancements from Incarnate Salvage, which I'm covering later in the "Life After (Level) 50" tutorial.)
However, if you were to slot an Uncommon Spiritual Enhancement, you would get not only the 33% Recharge boost, but another 33% boost in either Stun Duration or Healing, depending on whether you choose the Core build or the Radial build. (Core and Radial are just the two names for the differing "branches" of each enhancement type. This allows you to further customize your Alpha Slot enhancement choice, rather than having to go with a Healing enhancement you don't really need, etc.)
Slotting a Rare Spiritual Enhancement would net you either a 45% Recharge and 33% Stun, a 33% boost in Recharge, Stun, and Healing, 33% to Recharge, Slow, and Healing with a 16.5% boost to Stun, or even a 33% boost to Recharge and Healing with a 16.5% boost to Stun and a 20% boost to To-Hit Buff.
The Very Rare Spiritual Enhancement would either get 45% Recharge and 33% to Stun and Healing, or you'd get 33% boosts to Recharge, Stun, Healing, Slow, and Jump, and a 20% boot to To-Hit Buff.
Each of the Alpha Ability trees progress in this way, so there's a lot of customization room left for you to play with. You just have to determine what types of abilities you want to boost up and which you don't particularly care too much about. You don't have to have the rarest Enhancement to have the best character--sometimes, the more optimized build is about choosing precisely what you need and not wasting time building a higher-up Enhancement that you don't really need.