I know to enchant you must have a source of spell or magic effect in your abilities.

I'm looking to see if I can create a constant effect item for restore health, restore magicka and restore fatigue. Even at 1 point/sec it's a regeneration.

In contrast, is there a way to have a constant effect fortify magicka or would a constant effect fortify intelligence produce better results?

There is no restore magicka spell that you can learn without a mod, but the other two are possible. Fortify intelligence is done quite easily with potions.

It's far more efficient to create a short-duration Fortify Intelligence or Fortify *skill* than to make a CE for it. 1 or 2 points of long-term fortification is trivial, where getting a 10-20 point boost (or more) is significant. Potions, while one-time only, can be made several orders of magnitude more powerful, and far beyond the point of absurdity.

CE Restore Health or Restore Fatigue is well within the realm of possibiliy, and actually not that difficult compared to many other CE effects. Of course, ANY CE enchantment is nearly impossible with standard unfortified stats, and highly unlikely even with "slight" fortification ("slight" being anything under 100 points, "serious" being 1000 points or higher). A simpler alternative would be to pay a professional Enchanter, and then sell them some filled soulgems to recoup your funds.

I find the easiest workaround is to make whatever potions you need (in this case, fortify intelligence, or restore magicka), and also make feather potions. The feather negates the weight of any potions you want to carry, and you can assign your most-used potions to hotkeys (via F1 button), and it's as simple as one keystroke to drink your favorite potions. Yay alchemy!

I didn't know you could create a constant effect anything. How do you do that?

Kill Golden Saints and capture their soul in a grand soul gem, then use the highest quality gear/clothes/jewelry to hold the enchantment.
Any item can be enchanted, but the better the stuff (exquisite clothes & jewelry, daedric or glass armor) the more enchantment points available.

Use > 400 souls in Grand Soul Gems (or Azura's Star, for that matter). Golden Saints and Ascended Sleepers, for example, do fine. Then clicky in the bottom left corner to change Cast Once to Constant Effect. Notice the notable change for worse both in value and success percentage!

I haven't tried this yet, but I understand that if you drain your intelligence all the way, when it returns your magicka regens automatically. So try a 'drain intelligence' for 1 second. You couldn't really make it a constant effect, but you could tack it onto your favorite spells, so you'd never run out. Close enough.

Yes, this is true although the new CodePatch is going to eliminate it. One thing to note is that if you're a Breton, you have to double the drain because of their magicka resist.