The shade size will usually take up to a 150 watt bulb which is plenty for most uses. These lamps can be used on tall tables. Medium sized lamps can even work next of a sofa if the table is arm height and the room is not huge. Small lamps tend to be from about 15 inches to 20 inches tall and use bulbs from 75 to 100 watts maximum. These are used on bedside tables and other places where you don't need much light and there is not a lot of space.
Mini lamps are a special category.
They are usually under 12 inches tall and are more often used as an accent and for their sparkle and decorative function than to provide significant amounts of light. The remaining class of portable lamps is floor lamps and torchairs. The obvious advantage of these is that you don't need furniture to put them on, and they can provide lots of light wherever you need it. I also find it useful that they can be moved to give just the light you want where you need it, and then put back where they belong when you are finished with them. If all this seems like too much for you, it may be a good idea to use a home decorator or lighting designer to help you plan your home lighting.