Can someone give me a quick breakdown between the differences in the alchemic effects (restore, fortify, regenerate) and when best to use them? I've read the description and tested them out but am admittedly still a bit fuzzy.

restore is instant recovery of points, fortify is extra points on top of your normal max, regen is over time.

As stated above. Just to clarify, Fortification increases your max, but does not mean you have the full amount. In other words, you have a base of 200 Health, you fortify it 50 points, you have a max of 250, but you can get hit and have less health than your base amount.

Sounds trivial, but it can bite you in the butt if you end up losing 200 points of health in the above example and your fortification wears off, you will lose the extra 50 points and you will die.

Regen is a good tactic to use in prolonged battles so you don't have to quaff as many potions or spells along the way.

Also, I tend to use up or throw away the low level Restore potions as they weigh the same as the powerful potions.