EDIT: After further playtesting, I've found that the following changes let you leverage your economic advantage against Caprice and Ash remotes that are popular in the current meta:

Add: Vamp, 2 x Same Old Thing

Remove: Grappling Hook, Crescentus, Scrubber, Feedback Filter

"I play Calling in Favors for... 1, 2, 5... 7... 10... 12... 15 credits." - Me, just about every game with this deck

Background

Connection decks have been around for a while, but they weren't very impressive or competitive. When The Supplier came out connections-centered decks suddenly became viable. All those cheap connections are suddenly free! You can click twice to draw and install two things on The Supplier, getting your grip count back down to max. After Breaker Bay released this deck got a huge buff in the form of Off-Campus Apartments. Those 15-17 connections you want to install? They also grant you a card draw. In combination with The Supplier and Iain Sterling, the beginning of your turn sounds like this:

"I take 2 credits for my ID and 3 for Underworld Contacts. I install Compromised Employee for free on Off-Campus Apartments, drawing a card. Aaand for my 1st click..."

This deck has gone through a lot of refining over the past year, and I think it has gotten to the point where it can be played competitively.

Strategy

You don't want to run. Not at first. You're playing Iain Sterling for a reason. If you score you may as well be playing a blank ID with 10 influence. If you hit a snare, you might lose your only Corrodor or The Source. Let the corp get a few points on the board and then start applying some pressure. The only exceptions to this are when you are playing against Replicating Perfection and when you manage to find your Data Dealer quite early and you are pretty confident what the corp put down is an Agenda. Even if you wanted to apply pressure early, you don't really have the tools in this deck to do that effectively. Mulligan for Underworld Contacts and link (Hostages count as link, since you can tutor out The Helpful AI!) or for The Supplier and/or Mr. Li. Avoid getting flooded with programs since you won't have the cash to install them, and you definitely shouldn't discard them. You want to get to the midgame, stall, and then stop the corp in their tracks with The Source before they can score out the last agenda. Keep The Source on the table with Fall Guys if you need to and slam every single thing they install in a remote server once you have your economy flowing.

Thousand Cuts

You have Feedback Filter. Simply don't access unknown cards until this is installed. You also have Lemuria Codecracker. This let's you check Mushined cards on the table. Use Logos to tutor for these cards in the late mid game, and be careful about burning through your entire deck if you lost your Feedback Filter to Corp scoring net damage. Install programs as soon as they hit your hand, or you might never see them again (even if they do get trashed, you might be OK since these decks don't run much ETR ice). Use those HQ interfaces as net damage buffers, multi-access is dangerous.

Glacier

You'll want a few Compromised Employees installed before you start running. The corp likely intends to score out from behind a remote server. Let them score 1 or 2 agendas and when they try to sneak out that third one, Call in Favors and install an Overmind (preferably with E3) and start slamming servers. As long as you have a ton of money, there aren't too many cards in the game that can punish an AI breaker and a huge bank account. Femme Fatale will make sure you only pay the toll for Tollbooth once and Crescentus + Grappling Hook + E3 will shut down the huge ice you might see in Blue Sun like Curtain Wall, Hadrian's Wall, or even an Archer. Many of these decks run Bioroids, and E3 Feedback Implants eat through those easily.

Horizontal

Many decks these days aren't icing up their remotes. Scrubber is here to punish these decks. You will probably want to let the corp keep their asset economy around until you get yourself started. You need those initial 5 credits to set up Mr. Li, The Supplier, or your Underworld Contacts. It's a huge tempo hit if you run about trashing things. You can't get those credits back without spending your whole turn clicking for 1. Once you are setup, leave no card unturned. Run everything and trash it. If you have John Masanori and The Scrubber you'll be saving cash and drawing on your first run every turn.

Tag and Bag

Money is your Plascrete Carapace. As long as you can beat the trace, you are invincible. The Decoy is here to prevent the most common methods of tagging (doesn't work too well against Midseasons, for that you just need cash). If you suspect the corp is running meat damage. never access without having more than enough money to beat the trace! Even if they don't kill you with the tags, the damage they can do to your resources before Fall Guys are installed can be devastating. That being said, this is the strongest matchup for this deck. Eventually the corp will give up on killing you and won't have the tools to advance any installed agendas without you getting your paws on it.

Fast Advance

The Source helps a lot here. You may want to get it installed early just to force them to slow down and keep things on the table. You'll want to have Fall Guy's ready to keep it in play, however. These decks used to give Connections Iain a lot of trouble, but with Off-Campus Apartments you can get up to speed much faster and start applying pressure to HQ with HQ Interfaces.

RP

Not the best thing to see for any runner. You run into a bit of a problem with this deck because if the Corp scores a Nisei Mk II, you may never be able to get into their scoring remote again. If your meta runs rampant with these guys, try swapping The Source for a Vamp. The corp can't spend money on psi games that they don't have! I hear there are tools for dealing with the dreaded Nisei/Nisei combo in the next pack...

Why Didn't You Include X?

Some tempting includes might be Kati Jones, Sure Gamble, and Data Folding. But I've found that you simply don't need these cards. Sure Gamble just becomes silly when you have Calling in Favors in hand and Kati Jones requires too much attention that will just slow your set-up down. Also, the corp can easily judge how many credits you can get with Kati Jones on the table. It's much easier to catch the corp off guard with Calling in Favors and start of turn credits. You could have 3 credits on their turn and 16-20 after your first click. As for Data Folding, you won't always have the extra MU available in the late game and your ID with Underworld Contacts are usually more than enough to keep you going. One weakness of this deck is lack of multi-access on R&D. All I can say is: influence is tight. :(

Why DID You Include X?

• Peacock: You will have a ton of money. Peacock might suck. But it is in faction and deals with most popular code gates somewhat efficiently. E3 might be able to save you a few credits here and there with this breaker.
• The Helpful AI: This card is link. This card also turns your Hostages into potential link, making finding your link earlier much more consistent. Don't ask about the logistics behind taking an AI hostage in your apartment.
• John Masanori: The downsides of this card are mitigated by the fact that you will very rarely make an unsuccessful run with Overmind installed and a ton of cash, but also by the fact that you have Decoys and Fall Guys. This card gives you a lot of extra draw in the mid game that will keep your connection stacking engine going while applying pressure on the corp.
• Crescentus + Grappling Hook + E3 Have you ever seen the look on someone's face when you derez their Archer after paying a single credit to get through? You should try it sometime. Grappling Hook with E3 also let's you shutdown popular Blue Sun shenanigans without importing D4v1d.