If you can't cs well as a mage...

then don't buy Doran's Ring as your starting item.

Well, #1 advice would be to practice csing on your favorite champions, but let's just assume that for whatever reasons, you can't cs well. In this case, you must realize why Doran's Ring is a bad starting item. Starting with a Doran's Shield would be a much better item. Let's see why:

Stats comparison: Shield grants 20 more health, which is a decent amount early on. Last ignite ticks / last autoattack / last minion hit killing you can be avoided with the extra 20 health. Then, you sacrifice 15 AP and some mana regen for a quite strong HP regeneration effect. Honestly, the 15 AP isn't that big compared to the HP regen you can have instead. The mana regen is ok, but managing your mana to hit spells and harass your opponent is more important than this.

So, why does everyone start with a Ring then? Because of its passive. It grants 4 mana per minion kill. This is 24 mana for an entire wave. Paired with the % mana regen, they combo pretty well to essentially give you a free spell generally every minion wave, if you manage to cs well. Assuming you perfect cs for the first 5 minutes, you are getting 44 cs, which is equal to 184 mana. Now that's big, isn't it?

But that's if you are able to cs well. Even getting 35 cs at 5 minutes will grant you decent mana. Thing is, if you can't cs well, or if you die in lane and lose cs, then this item isn't worth it. You are not getting full value out of it. Making use of the bonus AP it grants is also a challenge. On the other hand, Shield start is so much more reliable. You just sit there and have bonus starting health, bonus HP regen and even more HP regen if you get hit by your opponent.

And here comes the kicker: the Shield also grants you +5 damage on your autoattacks vs minions! How awesome is that? Everyone has missed incredible amounts of minions on like 1 HP. This +5 is insanely important to help your csing with your AAs, which is the main waveclear early on anyway. Therefore, the Shield start will:

1. help you sustain better in lane
2. offer all its advantages with zero effort needed to obtain them
3. offer huge help in last hitting

Ring start offers:

1. stronger ability damage (not much though)
2. passive mana regen
3. mana regen on units killed (unreliable if having trouble csing)

Basically, Ring start requires you to have refined lane mechanics, knowing how and when to use your spells to take advantage of the bonus mana you get and rewards you for good csing. Shield start helps you survive in lane, while offering better last hitting. It is ideal when your laning mechanics aren't good enough, therefore having to do basically nothing to obtain the Shield's pros is very important.

This can also be applied, to a lesser extent though, on Doran's Blade for ADCs as well. If you can't really be constantly autoattacking to take advantage of the Lifesteal, then the item isn't that good. Again, having Doran's Shield as a start would be much better.