I use to PvP with my firesorc untill it expired. first off, i'm guessing this person isn't very rich, so alot of what xenon said doesnt apply to you.
Although, if your not going to have max block, spirit would be a better choice and is fairly cheap to make, or you might be able to get a 25% cast one for pgems.
Use a low end vipermagi, the +skills and 25+ res (for lowest) does much more to your damage then 15% fire damage, and is generally worthless without perfect resists.
nightwing? for a cold sorc yes, for a fireball sorc no! use shako, decently cheap, you can get one for a pul..ish, try trading your lidless and some other items for it.
Hoto is probably too expensive, use an occy, generally worthless as well, although its kind of like a mini hoto, 20% res, 30% cast, 3+ to skills, and +to str and energy, which is always nice. compared to the 40% res, 40% cast, 3+ skills of a hoto, it actually compares pretty nicely.
Belt: arachs is the best option, but its worth 1-2 high runes. maybe either trade ur nightwing for it, or just use a gloomstrap, the +%mana helps nicely i found untill you can get that arach.
if ur mana is low, use manalds, they give nice life + mana regneration, if you happen to find some nice rare rings with %cast, +mana +life, +str, +res, id use those instead though. the best rings you can get are sojs though, but are generally expensive to get 2 of them.
a good maras is probably the most expensive thing you'll ever need for this sorc, so try and get a rare ammy with +2 sorc skills, %cast, mana, life, str, res. if you cant find one, try gambling a 3+ fireskills one with cast (i think thats possible right? unless they are both prefixs)
The 105 breakpoint is the most important one to get to, technically you can get 25 from spirit, 30 from occy, 20% from magefists, 30% from vipermagi, and voila! 105 cast. all that for about 1 um rune.
Oh and by the way my old sorc had around umm... 40% faster hit recovery. (or less) from charms and never died from anybody except good chargadin glitchers and rarely 200% fcr lightning sorcs. (my sorc used sanc and didnt use treks either)
with spirit + sandstorm treks = 75% fhr, so just add in a few small charms and you can get that 86% if u want to.
Also, my sorc did not have anni nor torch, and only 3x fire gcs without life. (found em all myself

) all the rest of my inventory was jam packed with res charms, dex and str+ charms and lifers sc. and it was a hella fine sorc. the thing i like about the way sorcs duel is that it's usually up to the skill of the user then the gear you chose. compared to melee where its usually who has the best gear wins it all. Also my sorc had 8k fireball damage. It OBLITERATED everything except sorbers. and if they sorb, they deserved to be sorbed back. Also, why spend 7 hrs a piece for a 40+ fire lifer, (i think thats what they are worth now, east ladder, or was that light skillers, hmm) get regular skillers, usually worth around an um rune or less, that is if ur worried about damage. an average sorc with full fire skillers and anni and torch usually has around ~22k fireball damage minimum.
my gear looked like this
firefacet wizzy
sanc troll nest
upped 35% res umed viper
umed shako
33% maras
2x sojs
arachs
infernostride (i love these boots, i dont know why, they acutually suck big time)
magefists.
switch, cta lidless (didnt have enough str for monarch, all my points went into life and dex)
had about 350% stacked res for those blizzard sorcs with maxed cold mastery and lightning sorcs with their infinity merc, and anything else that likes to use -res gear. (some say its only nessecary to get up to 75% untill u face that blizzard sorc with facets sticking out everywhere, and a nice lvl 20~ ish cold mastery bringing u to -100% and taking double damage, while i sit in the blizzard feeling nothing)
my base stats were 150 energy with gear, ~200 dex, 118 str (with charms, not gear, to wear an umed templars coat) and about 125 vit (with gear,charms)(my sorc had memory staff and 1 pt eshield, no pts tk. some say its useless, i say its a life saver.
with all my charms and cta, lidless switch i had around 2.2k mana, 1.2k life. maxed res, maxed block, around 4.5k def, 105% cast.
200% cast is nice but ull be sacrificing 50%more mana, 5+ to all skills, +to attributes, 35% res, +mana, +life, 10% dr, an open socket (if u socket shako) and more just for 1 extra frame. although i guess u can always have that stuff in the stash for switch.
so, try and get some of that stuff i named above, those are probably just basic cookie cutter items, you will be able to duel, maybe not win so successfully as you want, but evetually the wealth does accumulate, and ull get those godly items to help u out.
have fun