Since OCTGN is a Weyland extravaganza right now, I've had the "pleasure" to play against Housekeeping about 10 games in the past 2 or so days. Here's what I've figured out:
What Housekeeping primarily says is: "Forget about luxury installs, re-evaluate your temporary/one-time solutions". In a way, the card helps you as the runner to learn to play better - you really, really need to install only the bare minimum of stuff you need to win. If you're the kind of deck that needs to set up a lot of stuff, you want to be installing in bursts (obviously), but don't get carried away - just because you won't pay an extra card for the second install now doesn't necessarily mean that installing the card is the right thing to do. Maybe it's better used as Housekeeping fodder for a future turn. I played mostly Anarch in those games, and the way I handled it was running on one Sucker and prioritizing real breakers over Parasiting stuff away. It was somewhat rough (because in a 6-agenda deck, Housekeeping sticks around for quite a bit), but in no way unmanageable.
Which reminds me - Housekeeping really makes those "one ICE solutions" (like, say, Parasite or Faerie) a lot less appealing. Sometimes it still makes sense to use them, because they're necessary, but in general you should probably be prioritizing a real breaker over them. The more mileage you get out of a particular install, the better - Kati over Daily Casts, etc.
Prepaid Kate has a good advantage in that she only has a handful of installables as part of her econ package (PPVPs, maybe a SoT or two), so you shouldn't be all that affected economically. If "outmoney them" is still your anti-flatline plan, you can conceivably risk a bit and go under 4 cards to get stuff done, as it isn't really affected.
Overdrawing is your friend, and Quality Time in particular is amazing - you would draw all those cards anyway, and presumably you'd ditch at least one of them anyway. This way, you just do it two clicks sooner.
Coupled with the Scorched threat (haven't seen Housekeeping out of Jinteki from anyone else, and I don't really know how it affected my opponents), Housekeeping means that every turn that includes installing probably needs careful planning and execution on the Runner's part (because installs become a 2-3 click affair), which helps the Corp predict what they're going to do.
Shapers seem particularly affected by Housekeeping, because their best tricks include installing stuff to be able to install stuff (SMC, Clone Chip) and/or re-installing stuff (Scavenge, Test Run). Going back to the "bare minimum needed to win" concept, I'd probably skip installing stuff like Clone Chip and SMC (beyond the 1 copy or so needed to get started), using them as fodder. Sure, you lose a bunch of flexibility, but it should be doable. Also, you probably have quite a few duplicates in your deck (console and spare breakers), you can use those for install turns. You might not get full value out of Kate's discount that way, but just pretend they played a Cerebral Static and you should be fine.