Most guitar sight-reading courses seem to start using open strings, and the C scale notes. At some point, one has to move away from open strings - in fact good players will rarely use them.
I advocate learning the major and minor scales up and down the neck, 2 octaves each, in one shape initially, so that if for example, the piece is in A, you'll be playing from fret 4 to fret 7 in major, and 5 to 8 in minor.This gives a good scope for most tunes, as most tunes don't encompass more than an octave or so. At least not in the easier, learner stages.Once you've found the first note, try to think along the lines of - the next note is 2 notes up from that one, so I move to the note 2 notes up in the scale.
To a great extent this obviates the need to keep thinking 'I must remember which notes are sharp/flat in this key'.You will know the notes that are relevant to the key you're in, so it will happen automatically. Obviously, accidentals will need to be addressed, but in the early stages they are not going to be that common. Once you get used to the concept, you'll be able to compensate.
After a while, move to other scale pattern in different places on the neck - bearing in mind the next one up will have its lower notes in the same place as the higher notes of the pattern below.
The 'problem' with guitars is that there are often several different places to play the same note. This can be alleviated using tab., but then you get to play where the tab says, which may not be the optimum place.