There are so many factors for choosing ice, I find it hard to decide what ice to include even when I already know what I want the rest of the deck to do.
First you need to know how many deck slots and how much influence you want to spend on ice, and roughly the total number of credits you want the Rez costs to be.
Then to decide how much Ice should gear-check the runner by ending the run, how much should hurt the runner for face checking it, how much is meant to tax the runner for going through repeatedly, and if there are any other jobs your ice can do.
Now do you play a lot of high strength ice? If you only have a few big pieces they can get by using D4v1d or Femme Fatale. Should you aim to exhaust their supply of Dave tokens?
Should you ever use ice with high cost but low strength, or is parasite too much of a problem? Could you potentially exhaust the runner’s parasites?
Then you have to be careful not to put too much Ice at the sweet spot of 4 strength or the runner can just use Atman.
On barriers you want a lot of subroutines because of Lady. On sentries it doesn’t matter as much because of Faerie and Switchblade. But you also don’t want to spend too many credits on any one ice because of emergency shutdown and crescentus. Unless you are using program destruction, you want a mix of ice types. Should you count traps in your total number of ice? Do you want to include the Ice that is specialised against AI breakers?
Should you just pick your favourite ice and leave it up to fate to decide?
This is way too broad a topic to address in one forum post. Would be a great full article for new players.
The biggest traps I see people falling into is going for synergy too much and focusing on the best-case scenario, instead of playing general purpose ICE with a strong average case.
What @Kiv says is basically true; I pick ice suites generally by worst case (breaking) scenario, the pace I want to allow the runner to run into my servers, and the pace my deck wants to run at. That’s hard to do. All of the questions you ask are legitimate, and the only way to know for sure is typically to pick what feels right and then change it up by testing alternatives over successive plays. Starting with middling efficient ice is a good point. But, I think your economy and pace also defines the type of ice and the investment you want to put into them.
This is one of the essential deck building questions and it’ll be different for every deck.
While not a guide to choosing ice, this article by David Sutcliffe covers different categories of ice functionality in Corp decks. What helped me was using it plus looking at decklists of the top Corp decks, to try understand why each different ice is in there. As @kiv said, generally you’d prefer having general purpose ice over speciality ice, such as positional ice (e.g. RSVP, Chum), or ice with a very narrow purpose (Lockdown).
You will be facing many different runners, and therefore ice that hates out specific breaker setups should also be useful against other runners. For example, Wraparound hates out AI breakers by staying at 7 strength, but still works as a gearcheck against other runners by forcing them to find their fracter.
The above-linked article is a good start for thinking about ice.
I find the best way to approach ice is by trying it out against a variety of breaker suites. You learn which ice is good vs which breakers in which kinds of situations. This helps tailor your ice to the specific deck.
I like to put ice in the deck that the runner can’t just bounce off, unless it’s really cheap. To this end, I prefer datapike, news hound, and quicksand/markus as gear check ice, and stuff like tollbooth or tsurugi or Heimdall 2.0 as good mid game ETR ice, and Janus and Orion when you need to drastically change the runners running habits late game, and that’s only if I’m sure I’ll have the money for them.
For fast advance, bouncing off ice is the worst thing you can do, since it then takes 2 more clicks to get past the ice if they have to install something, or 1 if they do some bypass trick like inside job, and that’s time you could be spending getting inside servers and oppressing r&d.
Kill decks just kind of want to have money and ways to ensure they can find the cards they need, so errand boy does there, as do the actual kill cards and ice, so really, depends on exactly what you’re trying to do.