Here's how it breaks down, yo.
For living single targets you can see, Stunbolt is almost always the best spell to use, with 2 exceptions. Against people with higher Willpower than Body, which is not super common (even mages are likely to only have, at most, 2-3 more, and many not even that), Powerbolt or Manabolt are arguably better, but also do more drain. In general, you should just be stunbolting in this circumstance. Against people with active Pain Editors, Powerbolt and Manabolt are outright better.
For groups of living targets all of which you can see, the above still holds with "bolt" replaced by "ball."
Against nonliving targets, things get complex. Indirect P-damage elemental spells are better than Power* spells in the following circumstances (note that Stun- and Mana- spells are useless here, also note I'm ignoring Counterspelling because it affects both equally):
Power spells fizzle if (hits < OR) and on average do (F+dicepool/3-OR) damage. Elemental spells fizzle if (hits <= defense) and defense is Response (for autonomous drones and vehicles) or Command (for remote-controlled drones and vehicles), and then they get soaked by Body+Armor/2.
Thus the failure chance is higher for the indirect spell if (Response or Command) + 3 > 3*OR. However, you only care about this if the failure rate is significant - 2% chance of a fizzle vs. 1.7% chance of a fizzle is whee! territory.
The average damage on a non-fizzle for the indirect spell is higher if 3*OR > (Reaction or Command) + Body + Armor/2.
Okay, that's some numbers. What does it mean? A typical nonliving target is going to be a drone or vehicle with OR 5 and Response of about 4. It takes Response/Command 12 before the drone or vehicle will have the same failure rate for an indirect spell as a direct spell. This means you are almost always going to have a higher failure rate for Power* spells. However, this difference gets less and less significant as your dicepool rises. With 15 dice, the direct spell is a terrible move because it will fizzle about 40% of the time. With 20 dice, your failure rate is about 15%. With 25 dice, it's about 5%. In any case, it's always going to be higher than the failure rate for the indirect spell except in major edge cases like a technomancer command rigging with a huge Command pool, and edge cases like the materials (from WAR!) with extra OR exist for direct spells too.
What about average damage? The direct spell will have a damage advantage on non-fizzles of (4/3+Body/3+Armor/6)-4. If you assume a drone with 3 Body and 9 Armor, the direct spell will do a bit less damage on average. If you assume a vehicle with 10 body and 20 armor, the direct spell will do 4 more damage on average. Moreover, the latter case matters more because you also need the extra damage more on tougher targets.
There are also three more catches. The first is that AE direct spells don't work on things you can't see. If you want to attack around a corner, or attack people hiding behind cover, you can center an Indirect spell somewhere you can see, and hit them - but you can't do that with direct spells.
The second catch is elemental-specific defenses like Nonconductivity. This only affects common elements, though, so can be gotten around by picking exotic elements like Light or Blast.
The third is the elemental effects. For the most part, these are things that are nifty like setting things on fire, and are reasons to pick one element over another, but not really reasons to pick an elemental spell in the first place. I know, I know, lighting things on fire is cool, but so is disintegrating them. The major exceptions are Metal, which makes you cut yourself if you take it because it blows trolls for pocket change, and Sound, which does S damage, ignores armor, and Nauseates anyone who takes more boxes than they have Willpower. Nauseate is 3 combat turns of not doing anything which removes people from the fight pretty effectively. This puts Sound attacks in kind of a different category than other elemental effects.
Okay, that was a lot of information. What conclusions can you draw?
TL;DR starts here
First, Punch, Clout, and Blast all suck. Don't use them.
Second, Powerbolt and Powerball are bad spells for anyone who doesn't have large pools with Combat spells. If you are a making a magician who's not very focused on combat spells, steer clear.
Mana* spells are very circumstantial spells. If you knew them, you would want to use them on living targets with either more Will than Body if you are willing to take extra drain for slightly better success rate, or on living targets with Pain Editors. Those are both pretty narrow niches, and they are only marginally better than Power* spells in those niches. Almost everyone should take Power* spells instead and spend the saved points buying more variety in their spells or more drain resist instead.
For heavily combat-focused magicians, Powerbolt is generally uniformly better than a single-target P-damage elemental spell.
For heavily combat-focused magicians, both Powerball and AE elemental P-damage spells have situational advantages and disadvantages. Buying either or both are reasonable choices.
That leave Sound spells. Single target sound spells cost 3 more drain than Stunbolt, and you are generally better off just overcasting the Stunbolt. However, there's 2 important advantages to Soundwave over Stunball - hitting targets you can't see, and that you can choose to cast Soundwave at Force = Magic and still have a solid chance of taking out everyone you hit, which you can't do with Stunball. Because Soundwave does more drain, you'll take the same damage as casting Force=Magic+6 Stunball, which would also flatten everyone but would do P drain. Thus, again, Stunball, Soundwave, or both are reasonable purchases.
My general recommendation for mages:
Everyone should know Stunbolt unless you just do not care about combat at all.
After that, buy some selection of the following, depending on how many of your spells you want to be Combat spells.
Stunball or Soundwave
[Powerbolt if Combat focused] [Any exotic P-damage Elemental single-target spell if not]
[Powerball or any exotic P-damage Elemental AE if Combat focused] [Any exotic P-damage Elemental AE if not combat focused]
After that, whichever of Stunball or Soundwave you didn't get, and whichever of Powerball or the AE Elemental you didn't get if Combat focused (which you hopefully are if you're buying this many combat spells).
After that, Manabolt.
Lastly, Manaball.
