I want to build a cybered adept hacker based on Frank Trollman's alternate Matrix rules, but I don't have much experience building hackers, and I'm still digesting the aforementioned rules. I could really use some help getting this character started.

I generally use 600 Karmagen, to approximate 400 BP. No special restrictions other than that I don't like blatant munchkinry; this isn't for a particular game.

The obvious choices for implants would be PusHeD geneware, probably also a nanohive with Neocortical nanites (you might want a cyberlimb for that one) and of course skillwires.
A cerebral booster may come in handy, as well as an Encephalon and a simsense booster.

Normally a hacker's best friend is the sleep regulator (hackers really need a lot of downtime to improve), but the Sustenance power is even better.

The key question is how many points of Essence you want to sacrifice.
I'd go for Magic 5 (3) and Essence 4, 3 points would be enough to boost your most important matrix skills by 3 points.

Combined with the right selection of skillwires and some of the mental adept powers from SM, it's easy to branch out from hacker to smartass skillmonkey at chargen or shortly thereafter.

You may also want qualities that help you save Essence, such as biocompatibility or probably even Type O system.
Make sure to balance your cyber/bio ratio for maximum efficiency.
For two points of Essence, that would be something around ~ 1.35 of either cyber or bio and 1.3 of the other.

For a more short-term game, qualities that increase your ressources (Born Rich, In Debt, Genetic Heritage) may look interesting.

What would you say is the best level to take skillwires at for an Essence-conscious build like this one? And is the Expert System worth it, assuming a decent Edge score?

At the start of the game, i'd take standard-grade skillwires at lvl. 3.
Under the Trollman matrix rules, you'll want to boost Logic as much as possible anyway, so at least for LOG-based skills, you'll have decent DP even when the skill itself is only at lvl. 3.
And that includes a whole hell of useful stuff- First Aid, Explosives, Chemistry, all the Mechanics skills, all Academic and Professional knowledge skills (like Weapons Design, Matrix Security Systems...) heck, even Arcana...with a build like that, you could spend your entire downtime crafting, healing and repairing.

Let's assume you get LOG 5 and add a Cerebral Booster (2), Neocortical Neural Stimulus Nanites (3) and PusHeD geneware- that would be 11 dice for anything linked to LOG, plus your skill rating.
You'll want your key hacking skills to be real, not from a soft, so you can enhance them with the adept power Improved Ability.
For the rest, even if you have an unmodified soft at only lvl 3, you already end up with 14 dice.
So i don't see a real need to get a higher-ranking system, especially as they require the Restricted Gear quality.

The expert system only lets you reroll your tests when you scored no hits at all.
If you plan on having a lot of skillsofts that still leave you with crappy dicepools, it may be worth considering, but if you use the wires mainly to add some dice on top of high attribute+bonus pools, i'd safe that room for something else.

Plus encephelon dice, don't forget those

Certainly not forgetting those, but an Encephalon is terribly expensive as far as both and Essence are concerned.
I'd rather go for other bonus sources first, especially under Trollman's matrix rules (by RAW, an Encephalon would be much higher on the list).
If you still want to squeeze out more dice after nanites, geneware, Cerebral Booster and Improved Ability, of course, go for it.