TL;DR

This is a reg-ass Apex deck. It plays Wasteland/Reaver/Chop Bot for money, and normal breakers. It does't play Apocalypse, instead relying on Heartbeat and Prey. It's actually kinda good, and below is a writeup of why I made the card choices I did. But first, here is what the world thinks of Apex:

I would start off by saying 'It's not the best time to be Apex.', but truth is, it's never been particularly fun to be Apex. Your breaker is bad against everything, and your signature event is better in literally every other faction. It's no wonder everyone is laughing at you.

That being said, it's hard to resist the challenge of trying to make a good Apex deck. I think this is pretty close to the best Apex deck you can make today. It's not amazing, but it's certainly better than you'd think based off the ID. I've now played 84 games (most in the competitive room, where I'd guess my winrate is something like 40-50%) with it for a sweet 55% winrate. That's kind of a meaningless number, sure, but it's probably the best way I have of assuring you I think this really isn't complete jank.

So who is deck for? It's for people who like playing honest, money 'n breakers Netrunner with a couple of tricks. It takes some time to set up a good econ engine, finds it breakers and then it wins games by running on servers and getting accesses. It's pretty strong against most varieties of kill decks, and can play a fair game against honest Corps.

The econ engine

The econ engine is the main reason to play this deck, and the reason it's not just a normal Runner deck played in a bad ID. Apex has two great cards in Wasteland and Reaver. Neither are unique, which means that in a fantasy land scenario, you can get 3 creds and 3 cards each turn - even on the Corp's turn! In practice, you don't actually want to do that, and in most games I find myself aiming for 1x Reaver, 3x Wasteland. To proc these on your turn, you use Chop Bot, which gives you an additional draw each turn. It's also nice to proc these on the Corp's turn, so you have 8 cards which can do so, and if they're doing any damage Heartbeat gets you a proc off that as well.

Next, you'll notice that even with only a single Reaver installed, this burns up your stack quite fast. So you need 1x Levy for sure. I play the second one fairly often, and having two copies also gets you a bit of a safety net in case of Ark Lockdown or just accidentally losing it.

The 2x Peace in Our Time is a recommendation of an opponent on Jinteki I forgot - sorry! I added it in very recently (within the last 10 games or so) - before that they were Fan Site and Spy Cameras. They've been doing great things for my setup, making it easier to use Sports Hoppers to dig and just actually trash important stuff early. It does cost an inf, which is sad because I'd love to have more Spy Cameras, but what can you do.

The breaker suite

Your ideal endgame is almost certainly going to be Shrike, Gordian, Paperclip supported by an Aumakua. The Endless Hunger is probably not going to be installed in most games, but it actually does a lot of work: it's great against Titan rush decks, a useful backup against Skorpios fracter sniper decks, and good against funky Loki/Mother Goddess ice suites. But in 'normal' matchups, you want to make money, play good breakers and be happy with your life. The Aumakua is pretty useful (unless they're on Chiyashi or something, in which case you should Chop Bot it) once you start getting in, so if I can find the time I like to install it. It can also just carry you if you happen to draw it early.

The tricks

Let's get the obvious omission out of the way: this deck doesn't play Apocalypse. This is, I admit, partially because I want to be contrarian, because hey, who can resist playing all of Apex' cards except the one which actually sees regular play? However, there's also a good reason for it - this is a deck which slowly builds an engine, then starts running. If you Apocalypse, you're throwing away your engine and kinda need to rebuild it. Apocalypsing will generally hurt you more than them.

Still, Apex does have some other tricks, they're just not as flashy. Hunting Grounds and Prey are very good against Corps who play ice. To stick to ice which I've seen played, Hunting Ground makes Data Loop, Komainu, Data Raven, Tollbooth and all the grail ice a lot less effective. In a pinch, you can also use it to look for your Paperclip and proc Reaver/Wasteland on the Corp turn.

As for Prey, it's excellent against Kakugo and Miraju both. If there's no annoying low-strength ice in the game, you can always save up some installed cards and Prey big ice too. DNA Tracker and FC3 are both kind of a pain to trash, but definitely possible. Hunting Grounds can also get you fuel for Prey if you need it.

Next, your coolest in-faction trick is probably Heartbeat. Having a Heartbeat installed does a lot for you. I don't think there's any console in the game I'd rather have. First of all, it pretty much single-handedly beats any Jinteki deck, as it makes stealing Obokatas pretty easy. You do need to actually take the 4 damage, but Heartbeat lets you absorb Kakugos, House of Knives, Prisecs or whatever on the way into the server, and also protects you from a possible Punitive followup.

Further, it just shuts down the Brain Rewiring/Show of Force combo completely. It's not a resource and doesn't cost 0, so there's no easy way of trashing it. I'm not yet sure whether you reliably beat Brain Rewiring CI, because apparently they can score out too, but you definitely stand a good chance.

Another surprisingly good trick is the fact that Chop Bot can remove tags. You rely pretty heavily on Wasteland econ, so floating tags is kind of dangerous, but Chop Bot lets you eat a Hard-Hitting News trace on low credit counts and still be able to clear the tags. With HHN being everywhere right now, this is pretty useful.

Finally, the perhaps best card in the deck is Spy Camera. It does so much for you. Provided you could get into R&D if needed, triggering a Spy Camera is effectively a free R&D access, saving you a click and the cost to break the R&D ice. But that's not all - it also procs Reaver/Wasteland, netting you creds and cards as well. By any reasonable metric, Spy Camera is easily the best econ card in the deck. If I had more inf, this would be my first priority.

The rest of the deck

Mad Dash is great with Spy Camera and TTW. Throw it away early, Levy it back and save it until you see an agenda with Spy Camera or you're going on a TTW dig.

Infiltration is great against shellgame Corps (although really, Heartbeat wins this matchup for you already), for seeing if the thing in the expensive remote is a 3/2 or just an Adonis, and also fuel for Aumakua. In a pinch, playing it for money is not awful with the amount of draw you have. It could easily be another card if needed, though.

Paricia is tech for the asset spam matchup. It's still not great, though, so it could be cut for another Spy Camera if you're inclined to just give up on it.

Fan Site and Shadow Net is a pretty cool idea courtesy of @SnakeEyes. Shadow Net is useful as tech against Shi-Kyu, Standoff, 15 Minutes and News Team, and also your only way to replay Levy if you accidentally lose it. It's generally going to become a Sure Gamble, though, for 9 easy credits, so I swapped it for Peace in Our Time which becomes 9 credits early on.

Finally, The Turning Wheel is your only source of multiaccess. Because you don't really want to start running too early, playing 1x is fine. I generally don't install it early unless I have early money and Aumakua.

About Sports Hopper/Reaver

3x Sports Hopper and 3x Reaver is really too much for the deck. Once you have even a single Reaver on the table, triggering Sports Hopper on the Corp's turn and then Chop Bot on your own will get you a total of 6 cards. That's probably a few too many, so I often end up installing Sports Hoppers face down.

Despite this, I think you should resist the temptation to cut any of them. In games where you don't draw your engine pieces, a Sports Hopper lets you set up faster, so I think staying at 3x is the right call. It's also situationally useful lategame in the cases where you lose a breaker and need to Levy and find it again ASAP, in matchups where the link is good and in cases where you need just a couple extra cards to steal that Obokata.

Finally, think carefully about how many Reavers you really need. There's no real point in drawing 3 cards at the start of every turn unless you're digging for something, so you probably don't need the second one. Installing 2x early and later trashing one might be good, though, but I generally feel okay putting the second copy of it face down.

Stuff you should test

You can in principle save influence both on the fracter and decoder. I think your best second choices are Saker and Black Orchestra. Black Orchestra has some merit, as the reinstall-from-heap is very useful, and Saker is interesting because there aren't that many good barriers.

I've also been considering trying to find space for a second Paricia. I feel like my games vs. asset spam depend heavily on whether I find Paricia or not, and because you don't really need all the breakers against those decks, having 2x Paricia is certainly possible.

Finally, just to make the accusations of blasphemy levied against me more credible, you could consider taking 3x Wasteland, 1x Reaver, 3x Chop Bot into Shaper instead. The inf spread works out, and you get a more interesting card pool to pick from. Just sayin'.