This is why I only use the most basic features of vim. There are simply too many commands to learn and many of these tutorial and cheatsheets present you with too much information. I don't think the time investment makes sense, and I don't understand why there has to be so much noise: how many of those commands save a significant amount of time; how often are they used? The questions I would like to ask advanced vim…
For instance, dt' will delete characters until it matches a'. But also, dtf' will delete characters until it matches a' but also delete that '. T and F goes backward.. you can put a number in front of the command to delete until it matches the nth ', etc. It looks like a lot of command.. but it's all the same basic ideas.
So to answer your question, yes you can use vim effectively with less than 10 commands.. but once you know those 10, it's a matter of seconds to learn 100+ which would make you extremely more effective.
And as my "top" commands.. I'd say definitely:
ciw *deleting the current word*
cit *deleting between the current html tag*
ci) *deleting between the ()*
With surround plugin:
ds' *deleting the surrounding '*
cs'" *changing the surrounding ' for "s*
/ *incremental search*
o/O inserting new lines.