First, regarding what to buy, if you were to buy at all:
lv 3 is better, until all the runes are lv 3 or higher, then certainly hold for summon.
The reason for this is that rune have "stat" and have "exp value" it is worth when used to lv up runes. lv 5 rune is 4x in term of exp value but not so much in terms of stat, not even 2x. If you have no rune of a certain type, for example, you can either get 4 lv3s, which is a lv 4 and 2 lv 3 across your 3 summon slots OR a lv 5, the 4+3+3 combo will provide almost twice the stat of a single lv5. Ergo, it's always better to buy the smaller one and make your runes more even than to have a "peak" lv 5 and then a bunch of 2&3s.
The reason to stop buying after having all lv3, once again, is the issue of diminishing return of stat per "exp value" of rune. To get to lv 4, you have to expend a full extra lv3, yet the extra stat provided isn't that of a lv3, but roughly half of it. The value diminishes further for lv5, which is less than 2x of the stat of a lv3 but requires 4x as much exp.
The reason he suggested to sell after getting all lv 5 is because this diminishes even further for lv 6. It would take another lv 5 rune to upgrade them to lv 6, which cost a full lv 5 which can be sold for 2400 token. On average, by the time you save enough for a summon, you'd have some frags in each and the cheapest one will only cost around 25k, which means you can get an orange summon for giving up around 10 upgrade. That said, orange summon over purple doesn't provide much stat, less than that of a lv 5 to lv6 rune upgrade. So if your team doesn't "demand" an orange summon for better chase combo, it's fairly pointless. The summons quest certainly doesn't pay off as it only give you a lv 3. So you should examine your team(or potential teams) and see if you will actually get to use the extra chase the orange summon can provide. An unused orange summon is a bad investment. But if your chase can be 1 or 2 link longer or can handle multiple initiation point etc as a result of getting an orange summon, then the stat loss is well worth it.
For as long as you do not yet need an orange summon or unable to afford it, don't buy ANY fragments at all. Sure it will take about 2 weeks to get it and starting early can get you it in a more timely manner, but the fact of the matter is that you might actually have it dropped. And for summons you already have, it's going to get converted to a far smaller amount of token than what it sells for. (this is, btw, why you should not have used ANY summoning scroll until you have captured all the blue/purple summons via the fighting method, if you haven't completed the set yet) Of course, if you KNOW you need a certain summon, know that you need say 26k tokens and have 24k on hand, you can certainly start buying it because chances are by the time you spent the 24k, you'd have the remaining bit to finish the purchase. Just don't start at say 15k, because that means you might have a bunch of summon frags converted to reduced value should you get lucky and pull it directly.