On many ships, basic inside and outside cabins are usually the same size, the difference being that one has a porthole or picture window to let in natural light. Balcony cabins can also be the same size as standard insides and outsides, with the addition of the outdoor space on the verandah; sometimes the interior space is larger. A basic cabin, regardless of category, is referred to as a "standard" unless there is something about it that makes it different (such as physical layout, being handicapped accessible or a designated family cabin). With minisuites on up, you get bigger and bigger indoor and outdoor spaces.
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.
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.