Act 1:
Keep an eye out for B-B-B links and one B-B-R link
Optionally look for a single B-B-G link
Pick up sapphire rings for merveil and wand vendor recipe
(can also pick up iron rings for the sapphire ring vendor recipe)
Sell Armourer Scraps and Blacksmith's Whetstones for Wisdom Scrolls
Sell magic items unidentified for transmutation shards
Sell rare items identified for alteration shards
Kill Hillock in the Twilight Strand
Enter Town - Grab Freezing Pulse, link with Arcane Surge
(Buy a second Arcane Surge, keep both Arcane Surges at level 1)
Mentally Prepare yourself to die 10 times to Rhoas, because GGG overtuned Act 1 and all the rares have frostweaver.
Unlock the Submerged Passage Waypoint
Kill Hailrake in the Tidal Island
Enter Town - Grab Flame Wall & Frost Blink, link together with the second Arcane Surge
Grab Holy Flame Totem & Summon Phantasm, link together
Unlock the Prison waypoint
Enter Town - Grab Added Lightning Damage, link with Freezing Pulse & Arcane Surge
Grab a second Added Lightning Damage, link with Holy Flame Totem & Summon Phantasm
Kill Brutus in The Prison
Enter Town - Grab Clarity
Grab Flame Dash to replace Frost Blink, link with Flame Wall & Arcane Surge
Grab Vitality (optional, can be difficult to meet strength requirements, but taking practical application early on will help)
Unlock the Cavern of Wrath waypoint
Enter Town - Grab Arc to replace Freezing Pulse, link with Added Lightning Damage & Arcane Surge (hold onto volley for topaz ring vendor recipe)
Grab Orb of Storms, link with Added Lightning Damage
(At this point we can stop using Flame Wall and Holy Flame Totem, however the totem is still nice early on for life regen from consecrated ground)
Do vendor recipe for flat added cold wands. (magic/blue wand + sapphire ring + alteration orb | Note: the wand will retain socket links and colors)
(If you don't have sapphire rings you can vendor 1 blue gem + 1 iron ring to obtain a sapphire ring)
Kill Merveil in Merveil's Caverns
Act 2:
Pick up Topaz rings for vaal overseer and wand vendor recipe
(can also pick up iron rings for the topaz ring vendor recipe)
Kill all Bandits
Kill Fidelitas in the Chambers of Sins
Enter Town - Grab Herald of Thunder
Grab Herald of Ice (Optional, can be difficult to obtain dexterity requirements)
Kill The Weaver in The Weaver's Chambers
Enter Town - Grab Controlled Destruction, link with Arc & Added Lightning Damage
Grab Controlled Destruction, link with Orb of Storms & Added Lightning Damage
Unlock the Caverns waypoint
Enter Town - Do vendor recipe for flat added lightning wands if you haven't yet, using a magic/blue or preferably rare/yellow ring.
Kill the Vaal Oversoul in the Ancient Pyramids (The Caverns)
Act 3:
Save all 4-links in your stash, you never know when you might need one.
Keep an eye out for
B-B-B-R (Lightning Conduit),
B-B-B-G (Crackling Lance or Wave of Conviction, before B-B-B-B hydrosphere)
B-B-R-G (Storm Brand)
B-B-R-R (Flame Dash/Molten Shell)
B-B-B-B (Hydrosphere Hextouch)
Enter Town - Grab Conductivity
Grab Wrath (optional, probably will need to replace Herald of Thunder and I'm not sure the reservation difference is worth)
Help Siosa in the Library
Head back to Nessa in Act 1
Grab Storm Brand and two Unbound Ailments
Head back to Yeena in Act 2
Grab Elemental Focus
Grab Faster Casting (optional, don't worry about this if you don't have a spare B-B-B-G)
Head back to Clarissa in Act 3
Grab Crackling Lance or Wave of Conviction
Return to Siosa
Grab Inspiration, link with Added Lightning Damage, Elemental Focus & Lightning Conduit (Keep using Arc until you have your first Ascendancy)
Grab Crackling Lance & Onslaught, link with Unbound Ailments (& Faster Casting, optional)
Grab Increased Duration & Onslaught, link with Storm Brand, & Unbound Ailments
Grab Increased Duration, link with Flame Dash & Arcane Surge
Optional:
Grab Determination or Grace (you CANNOT run Wrath, Herald of Lightning, or Herald of Ice if you use one of these)
Grab Molten Shell, link with Increased Duration, Flame Dash, & Arcane Surge (Molten Shell isn't very good without Determination)
Act 4:
Complete both Kaom and Daresso's Dreams & Help Dialla activate the Cannon unlocking Belly of the Beast. (Might be after killing piety, but I think next gems unlocks before)
Enter Town - Grab Hydrosphere, Increased Area of Effect, and Hextouch
Replace Crackling Lance setup with Hydrosphere, Increased Area of Effect, Hextouch, and Conductivity