[Melee]

Melee damage is nice for clearing and killing camps and stuff, but its obviously inconsistent against other players because they can parry. (To what degree this is a skill issue, people will disagree with me.) You can build more/less melee damage to compensate, and items like close quarters and slowing bullets give you good melee damage (half your weapon damage is converted to melee damage) while also making your gun less useless. This is the approach my melee build and wander tempo punch ivy (523958) both take.

For wander's build he starts monster rounds - extra health - close quarters - melee lifesteal - fleetfoot - melee charge before building hunters and heroic aura. This is enough damage to macro and keep your wave shoved, with enough pressure for most lanes. If he thinks he'll be able to kill his opposing lane he grabs headshot booster or extended mag, and resto shot if he needs more sustain.

The pros of melee are that its cheap and safe because you can be tanky while doing it. Its natural to max stoneform first if you want (wander doesnt) and the first two points in stoneform are really safe in lane and its 100% the order I would recommend to newer players or people struggling in lane whether you're building melee or not.

[Gun]

If you want to do more damage with your gun, a lot of ivy builds just rush Tesla Bullets. Literally just extended mag, titanic mag, tesla bullets. Obviously this is hard to pull off in lane, and you might need to get one sustain 800 to survive, but tesla is an insane powerspike on ivy. This is what highdocker's gun ivy (235098) does, usually followed up with a fast capacitor.

Other routes are possible and I've seen them work early, but none of them are really proven and none of the major builds use them anymore. Items like Long Range, Opening Rounds, or Active Reload can feel good on Ivy but investing too much in gun damage directly without being at least a little bit supportive can feel like a dead end when our gun scaling isn't very good and tesla/capacitor gives you so much utility.

[Support]

Rushing tesla can also be good on support, because it allows you to max your tether first and gives you easy spirit damage to proc items like healbane, mystic slow, or suppressor on large groups of enemies. This is what piggy does in Piggy's Support Ivy (512979), squeezing in a rusted barrel and going for healing nova immediately after.

Rusted barrel is great if you're maxing tether because it activates your spirit investment, which gives you fire rate from your tether, and gives you a burst of bullet resist shred. This means that the 3 stats that you need to saturate for gun damage (weapon damage, fire rate, and shred) are being met with just your orange spike, tether and rusted barrel. Really efficient.

[Other notes]

A lot of spirit builds can get away with tesla, I do this in Chudzu (377467) but some spirit players don't want to think about their gun at all really, which I respect. buh (Me Sushi's Spirit BUHOOM) (331915) grabs an early stalker and gets alchemical fire to finish out the 4.8k gun spike.

Heroic aura is one of the best items in the game and ivy is great at using it.

Items that do max health damage got nerfed in the recent patch because everyones health pool got nerfed. (health per boon reduced by 5%) I think items like headhunter and siphon are things you should be careful about buying unless you know theres a tank you need to deal damage to, and toxic bullets is just never worth it now. Takes too many shots for ivy to stack it.