Getting into petrochem for the first time is difficult, and while cracking naphtha is alluded to by the existing quests, many of the products aren't discussed at all (despite some being necessary for later quests), which can be confusing for just getting started with petrochem just from how many new things are introduced at once. In my playthrough, I've had my text editor and draw.io open constantly to try and figure out the math for each of these products and how to put them to best use.

Three products are needed for specific quests:

• Benzene and butadiene are needed for butadiene-styrene rubber, which is (as of the nightly build from f378b4f) required to produce LuV and higher conveyors (silicone rubber is not accepted), which are necessary for core progression. The ratios involved - there's no way to produce butadiene without producing more benzene than is needed to make rubber - also mean that excess benzene must be dealt with somehow.
• Toluene is needed for TNT, which isn't strictly necessary versus dynamite, but does have a later quest.
• Propene is needed for the existing allyl chloride quest, providing an alternative route to resin compared to biodiesel/glycerol. Whether it requires its own quest really hinges on the handling of the above few.

Other things to note about other products:

• In my experience, the best use for benzene outside of butadiene-styrene rubber is producing dichlorobenzene -> phenol, which is chlorine-neutral and helps complement the propene -> allyl chloride -> epichlorohydrin route referenced by existing quests. This is just as efficient for benzene:phenol as other options, while requiring less energy than the direct conversion at EV, and not being a sink for phosphoric acid like cumene. (Honestly, the cumene process should return a reusable amount of "diluted phosphoric acid" or something of the sort - its IRL role in the reaction is a catalyst, so it should be able to be reclaimed somehow. As it stands, phosphorus - and arguably propene, as an epichlorohydrin source - are more valuable than acetone, especially with how easy it is to produce the latter from calcium acetate in 1.3 even at MV power).
• Butene cracking is one of the cases where I've found steam-cracking preferable to hydro-cracking. From heavy fuel feedstock (80 mB butene : 50 mB butadiene), cracking the butene yields enough ethylene to completely convert the butadiene to rubber without tapping the primary ethylene output, while it comes very close (less than a 5mB difference) from naphtha feedstock (50:50).
• Propane can be centrifuged for LPG, though I'm unsure if this is more energy-efficient than hydro cracking it down to methane and burning that now that sodium hydroxide can be electrolysed (reducing the energy cost per bucket of hydrogen). In either case, gas turbines can help reduce a refinery's energy demands.
• Ethane should be hydro-cracked - steam cracking produces carbon but less methane, and carbon is easily sourced by other means.
• Methane and ethylene are core production chemicals that don't need an introduction by the time someone is steam cracking anything.

It might also be worth mentioning in the quest for distillation towers that adjacent towers can share walls, as long as they don't share any hatches; this can be done with up to four towers in a square shape, and significantly reduces the amount of stainless steel investment needed to get into petrochem/charcoal byproducts at the MV/HV boundary: