Very few ships actually have cabins dedicated to solo travelers. These will have sleeping space for one and can be quite small. The studio cabins on select Norwegian ships are the most famous example of this: The 100-square-foot staterooms each contain a full-size bed, nifty lighting effects and a large round window that looks out into the corridor. If you are a solo traveler, you will want to price out the cost of a solo cabin (usually somewhat higher than the double-occupancy rate of a similarly sized stateroom) compared to the cost of paying the single supplement (an extra fee tacked on if there are not two people in a cabin; the price can come out to as much as double the regular rate) for a standard cabin. And book early, as solo cabins sell out quickly.
For some reason, most cruise lines assign their nicest and most expensive cabins to the highest decks, usually just below the pool deck (most likely because if you have a window or balcony, you have a more sweeping vista). Still, it is the pool deck that often causes the most noise problems, so if you do not want to hear scraping chairs at the crack of dawn or yee-hawing pool parties until the wee hours, go down a level. In fact, when it comes to noise, the best bet is to select a cabin that is both above and below other cabins.
Cabins are priced based on location on the ship. Typically cabins on lower decks are less expensive. Typically cabins midship (in the middle part of a deck) cost higher. Balcony and Suite cabins on the very aft of the ship can also be more expensive than other cabins.
If you tend to get seasick, cabin location is really important. It is a question of engineering, really. The lower and more central you are in a ship, the less roll and sway you will feel. Even if you choose a balconied stateroom, choose the lowest level and the most midship one you can find. The higher decks and cabins at the very front (forward) or back (aft) of the ship will rock and roll the most.