The ring of mystic fire only affects the upcoming spell once

The ring of mystic fire (Magic Item Compendium 125) (7,500 gp; 0 lbs.) does, indeed, grant "a bonus to the amount of damage you deal with the next fire spell you cast before the end of your turn," but the ring only grants that bonus once. Each ray of a scorching ray spell isn't the spell; instead, the whole spell creates multiple rays. The ring improves the spell's damage only once by a maximum of +4d6 no matter how many effects result from the ring-modified spell.

(Ruling that each ray of the scorching ray spell benefits from the ring multiplies the power of the ring by the number of rays—with rather extreme consequences at low levels, especially given that the ring increases also the wearer's caster level for fire spells!)

Although the DM has several options available to adjudicate the ring's effect—allowing the player to distribute the total number of extra dice damage the ring grants among the rays before (or even after) the rays're launched, for instance—, this DM would keep things simple and have the player add the extra damage to his PC's first ray in a volley from the spell scorching ray, in much the same way that precision damage applies to the first attack in a similar volley (Rules Compendium 42). (In fact, I have a fire wizard in a current campaign who's eyeing this very item, and that's how I'm ruling it works.)

Hence, for example, under such a ruling, a level 6 caster wearing a ring of mystic fire can take a swift action to spend 3 of the ring's charges. Then the caster can cast scorching ray, creating 2 rays (because of the increase in caster level granted by the ring) and making 2 ranged touch attacks. If the first ray hits, it deals 8d6 points of fire damage. If the second ray hits, it deals 4d6 points of fire damage.

The pros of Scorching Ray are:

• Assuming no attacks miss, it does more damage than Guiding Bolt.
• You have the option to attack multiple targets when using Scorching Ray.
• Eventually, when you have higher level spell slots, it will scale much better than Guiding Bolt.
• Scorching Ray works with the Elemental Adept feat - which allows you to ignore fire resistance and raises the floor on your minimum damage. (Credit - yinzanat)
• Against enemy spellcasters, Scorching Ray provides more opportunities to break their concentration. (Credit - gburton)

The cons of Scorching Ray are:

• It deals fire damage instead of radiant damage. While this is situational, there are more monsters in the Monster Manual that resist fire than resist radiant.
• It does not grant advantage to the next attack roll against your target.
• If you have advantage for being hidden it will not apply to your second and third attack.

The thing that could be either, depending on how superstitious you are about your dice (and what the AC of your target is):

• Scorching Ray makes three separate attack rolls.

You would want to use Scorching Ray if:

• There are multiple targets that you are confident in your ability to hit.
• You are fighting something that is vulnerable to fire damage.
• You need to deal more damage right now.

You would want to use Guiding Bolt if:

• You need to set an ally up for an upcoming attack against the same target.
• Your allies are having a hard time landing attacks against the target.
• Your next ally to attack is a rogue who will get sneak attack damage from the advantage. (Credit - DaleM)
• There is only one target. (You may wish also just not upcasting Guiding Bolt in this scenario and relying on your party to use the advantage.)
• You have advantage on this attack (ie you are hidden).