I have done each of the four (card, call, text, and email) in the past 2 months for 4 different deaths. Each depended on my relationship with the person and their age.
Everyone is different and I think age of receipt has some to do with it but when my dad died I felt like
-cards were wonderful but they were more “long term” or formal and were kind words but not immediate. Good for ANY level of acquaintances
-calls I did not want to talk to anyone except immediate family. When I got caught on the phone by a good friend I spent more time trying to hold it together than anything and I was in no mood to discuss how I was doing. A call a few weeks after the fact to check in can be nice.
-text I know I know it seems so tacky BUT texts were the perfect way for close friends and clos acquaintances to say “so sorry we just heard, please let us know if we can do anything/can we drop off dinner/Pick up kids/etc) and those were the easiest for me to respond to when we generally did need help (can you come babysit while we run to the funeral planning, would you mind handling carpool for kids sports tonight, we could use some snacks for all the people dropping in, etc). Those texters also followed up with cards or came to the funeral too so it wasn’t the only communication just the most immediate and most helpful. I think this CAN be a god option for closer people and people that already text back and forth
-email was just as good as cards for those that didn’t have my address (work colleagues mainly)
Visitors and deliveries were a hard no unless we had texted about dropping something (or a kid) off. The house was borderline chaos, we were in and out all day and night, and sometimes when we were in we were curled up on a couch crying together.