Well science consoles for the most part give a bonus to a specific Captain skill. So you first need to find out which Captain skills(s) (if any) affect the abilities you are interested in. That information you can find in two ways.
First is to look at the information on the Powers window (while you are in space, hit 'P'). The information pane will tell you which captain skill affects that ability on the bottom of the text. The second way is to use the ability filter at the top of the player's skill window. Select a character or BOFF and then select an ability. The skills that affect that ability be lighted with a dotted line outline around the skill box.
And from there match the skills the Science Console boosts to the Captain Skill that you need for the ability. Things have been vastly simplified with the new skills tree.
And as to which shield? Well that depends, most people tend towards the Covairant shields which have a lot of damage capacity but they regenerate very slowly. Another is the Resilient Shields. Resilient shields have slightly less capacity and regeneration rate than a standard shield, but a Resilient shield will neutralize 5% of damage, and that means only 5% bleed through damage. Last type are Regenerative shields. They have less capacity than a standard shield, but much higher regeneration rate. You need to run your Shield Subsystem power very high to boost the regeneration rate.