Major skills are those that have 6 boxes on the character screen: Endurance, Melee, and Ranged.
The Professional achievement will come naturally as you play, provided that you do other quests as well. You should be able to collect it between levels 18-20, depending on how you allocate points.
If you're not sure which skills you should max out, I recommend choosing Endurance to start. This will increase your health and allow you to have more implants. Another achievement is related to implants, so it's very important that you upgrade Endurance to the fullest, otherwise, you might not have enough room for all of them.