I have sung for years but am finally getting round to playing an instrument for the first time. I have checked, but there are no teachers for it in the area.

I want to build up my sight-reading in particular as well as being able to play the thing. So what is the best way to go it? Do I concentrate on a few tunes and get the timing right?   Or do I try lots of tunes so I am forcing myself to read the music more, rather than learning the specific fingering for one or two through tunes over and over, but not really knowing the note positions? Or do I forget about that instrument and go with something that I can find a teacher for?

I expected to find this had been discussed to death, but I didn't find a thread with a quick search.