Bulbs come in standard sizes. Thus from your description a 24 watt, 12" bulb with pins only on one end is going to be a 24 watt power compact. The pins on the end can either be straight in a line or in a square formation. The bulb in your hood is connected to a ballast which drives it. The ballast it rated to drive that bulb which has certain wattage in this case 24 watts. Even if you could find a different wattage bulb that fits which is unlikely the ballast is going to provide the same power, that being 24 watts.
This is a 20 gallon you said. IMO your current lighting should be fine, 1.2 watts of power compacts is a pretty good level. Just pick plants that are low-medium light and go from there. Especially for a first planted tank don't go too crazy with the light level. The more light above a tank the harder it is to balance and manage, normally they need more maintenance as well.
You should fix some sort of condensation protector over the bulb compartment. It depends on how the hood is designed... but plexiglass is one method. IMO no bulb should be exposed to water unless its a good distance from the surface to the point where it escapes condensation. Ballasts are high voltage, I'm not sure how manufactures get away with leaving them exposed to water. Well I my only tank that has a fixture that was originally expose to the water simply says "to reduce risk of shock don't touch when wet" lol.