Conductor of Nephthys allows you to basically access your whole Nephthys line while also putting cards in your hand to make up for the losses caused by the Nephthys cards having to destroy cards in your hand. While they may not be good for starting your combo, they are good to get more material for extension. And with Conductor being able to summon Cerulean Sacred Phoenix of Nephthys, you have a way to clear a board of monsters going second and being able to recuperate losses the following turn. A lot of the Nephthys cards are either just bad or don't do anything productive. Chaos Nephthys and Dark Nephthys just suck. Sacred Phoenix of Nephthys hurts you more than the opponent because it destroys your set Smashers, Starters, and Double Cross. Matriarch of Nephthys does Summon back a Nephthys in GY, but Devotee can already summon herself back and doing any more will just fill your board with monsters that do nothing. Chronicler of Nephthys is only good if it is destroyed, so it isn't good to run.
For the Spright part of the Deck, it is the usual 3 Nimble Beaver, 2 Nimble Angler, 3 Spright Blue, 3 Spright Jet, 1 Spright Carrot, and 1 Spright Red. Blue searches Spright monsters, Jet searches Spright Spell/Traps, Carrot is a Spell/Trap negate, and Red is a monster negate. Beaver and Angler are a good way to start your combos Normal Summoning Beaver gets you a Level 2 and an Angler from Deck. Or you can send an Angler from Deck to GY with Sprind in order to get 2 Beaver from Deck. The important thing to remember is that Angler can also trigger when sent from hand which means that it can trigger off of using it for a Ritual Summon or destroying it in hand for Nephthys monster effects. 1 Cerulean Sacred Phoenix of Nephthys, 3 Devotee of Nephthys, 3 Conductor of Nephthys, and 3 Disciple of Nephthys. Going first, Cerulean Phoenix is a garnet for situations where you make Nephthys, the Sacred Preserver in which case you can save it for next turn or you can use it as a Nephthys card in hand to destroy for an effect. Going second, it can pop Nephthys cards on the field and in the hand to destroy an equal number of monsters your opponent controls, and if it destroys itself, it can bring itself back. Devotee is a Pre-prep target and something to summon off of Conductor for free. It also summons a Nephthys monster from Deck on Ritual Summon and can bring itself back by destroying a Nephthys card in hand. Conductor summons any Nephthys Ritual from hand or Deck on Ritual Summon for free which is usually going to be Devotee as this counts as a Ritual Summon. Then, when it is tributed or destroyed, you can destroy up to 3 Nephthys cards from hand, Deck, and field except Rituals next Standby Phase. You usually destroy Disciple for a Spell/Trap search next turn. Disciple is the only worthwhile non-Ritual Nephthys to play. It can destroy a card in hand to add a Nephthys monster from Deck and it searches a Spell/Trap during the next Standby Phase after it is destroyed. Lastly, we have 2 Ash Blossom & Joyous Spring and 1 Diviner of the Herald to Summon off of Gigantic Spright to get the missing pieces of your Nephthys combo.
3 Spright Starter which is E-Tele for Sprights. 1 Spright Smashers which is a banish. 3 Pre-Preparation of Rites. 3 Rebirth of Nephthys which is the Nephthys Ritual Spell which can be searches with Pre-Prep as it mentions Cerulean Phoenix and Devotee. 3 Infinite Impermanence and 1 Spright Double Cross.
For the Extra Deck: 1 Herald of the Arclight to send off of Diviner. 1 Divine Arsenal AA-ZEUS - Sky Thunder. 1 Downerd Magician. 1 Onibimaru Soul Sweeper. 2 Gigantic Spright. 1 Number 2: Ninja Shadow Mosquito. 1 Number 29: Mannequin Cat. 1 Mekk-Knight Crusadia Avramax which you can Masquerena into. It prevents your opponent from targeting other cards you control for attacks which really helps out in Spright and it clears the field of things like a spent Sprind or the Sacred Protector that is still sitting on your field doing nothing. 1 Knightmare Unicorn. 1 Nephthys, the Sacred Preserver. This can either search a Level 8 Winged Beast from Deck and add back a Ritual Spell from GY or it can destroys a Nephthys card it points to and summon a Nephthys monster from GY with a different name. You usually use the search effect to get more cards into your hand that you can destroy for your Nephthys monster effects. 1 I:P Masquerena, 2 Spright Sprind, and 1 Knightmare Phoenix.
Side Deck is just some going second cards and removal options.