This is a work in progress. Please take with a pinch of salt atm…
I recommend the following way to get to 150 Agony Resistance so that you can do T4 Fractals….
This assumes that you will eventually have the full 18 infusion slots though so you might want to use just +9s all over if you don't think you will do this or just want to get AR as quickly as possible. e.g. if you don't infuse your rings or your back item, you will lack 3 slots and therefore have only have 15 slots (15 x 9 = 135). You can gain +15 AR from a tear of alba (or +10 if you don't have the mastery).
The fractal golem merchant will only sell AR infusions that give an odd number of AR. So you will need to get +8s by either crafting two +7s or buying them from the TP.
I recommend focussing on getting ascended trinkets (especially an amulet and 2 rings) and weapons first. They are the easiest to get and provide a large benefit. Although the amulet doesn't have an infusion slot (it has an enrichment slot which is different), it provides a lot of attribute points so the difference between an exotic amulet and an ascended one is quite big.
Each ring will provide you with one infusion slot to start with. If you have the Heart of Thorns expansion, learn the Agony Channeler mastery as you can then “attune” each ring (it's cheap) for an extra infusion slot. You can also "infuse" the rings for another extra infusion slot but it's much more expensive so you might want to do that later.
Put one +9 AR infusion in each ring and +8 AR infusions in the remaining infusion slots (if you have attuned and/or infused them).
Put +7 AR infusions on every ascended (or legendary if you are fancy) weapon (1 for one-handed weapons, 2 for two-handed weapons). You will only get the benefit of AR in infusions in the active weapon set. We put the cheapest infusions in the weapons because you need separate infusions for each weapon that you are using and, with weapon swapping, this will mean at least 4 infusions, more if you use other weapons sometimes or want to use ascended underwater weapons.
Now focus on accessories and armour. Accessories with core stats (berserkers being the most popular) can be purchased with guild commendations - join us for TooT guild missions to earn these! If you want stats like maraurder's or viper's, consider Living World maps or the stat-changeable Mist trinkets. Put +8 AR infusions in both accessories and all pieces of armour.
Lastly, infuse your back item (removing the existing AR infusion first) to give it an extra infusion slot and add another +8 AR infusion.
Personally, I think these are a waste of money. A +9 AR infusion that also provides +5 attribute points is a lot more expensive than a regular +9 AR infusion. Focus on getting 150 AR first and then if you really want to push for getting potentially another 18 x 5 = 90 power or condition damage or whatever, then gradually start collecting them.