Nope, you got that mixed up. Series wound is the most common motor type for DIYers.
Expensive.
Nope, got that one mixed up too. An AC-MOTOR has higher efficiency than a series wound DC-motor but an AC-CONTROLLER has lower. In the end the difference is generally to the AC systems advantage, but the difference is also generally speaking pretty small when you consider what you get for your money. Buying more batteries to compensate is usually more economical.
For more details I recommend the search function. This topic has been convered several times in this forum in more or less friendly tone...