dogperson makes a very important point, in defining a difference between what is sight reading, and what is reading. They are both forms of reading and a stage in learning music, but come with different goals and approaches.
Sight reading or prima vista, is playing through a piece without any prior run through or opportunity to practice. The aim is to convey the salient aspects of the piece, at a reasonable tempo, with fluency. In such case, the decisions in choosing fingering would lean toward making the workflow as efficient and fluid as possible. They may not be the best musical fingerings, and they may not be the ideal performance fingerings, but they should at least be functional fingerings.
For reading, the musician may be at one of the learning stages, but has had prior opportunity to read and play though sections of the piece. At this stage one could be working out what the best fingerings for their hand are, and in doing so may isolate sections of the music with difficult fingerings in order to work through them.
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When reading intervals it can be beneficial to develop a sense of visually estimating the interval, as opposed to trying to read the exact interval in a single glance. The exact interval would eventually be identified after a series of layers.
For example: A third is either two notes on lines, or two notes in spaces. It is a third regardless of what accidentals precede it or what the key signature is. Even if you can't decipher at first glace what the exact notes are, you can easily visually estimate a third, and prepare by forming the shape of a third in your hand.
Become adept at recognizing important larger intervals such as 4ths 5ths and octaves, and how they look on the page. You can use these as markers to give you a direction when reading intervals in their vicinity.
For example: You see a large interval, you first ask is it an octave? If yes, you are done, if no, then ask is it smaller or lager than an octave? and so on... This gets you in the ballpark quicker than trying to accurately read the interval in a single pass.
Similar to reading a map. Find the general direction, north, south, east or west. Then refine, is it closer to north or closer to west, is it NW, or NNW? So now that we know the direction, what are the best streets to get there.