There is nothing wrong with a DA40 although there has been plenty of concern expressed on here regarding the Theilert engine. Many schools using the aircraft are finding that their fleet are becoming unflyable as parts are required for the engine but are not available or too expensive. You may therefore want to be caution about whether you find you are unable to continue your training in the 40 part way through and have to change to another aircraft. If this is a concern you should read the various threads on the subject which will give you a better understanding of the current and possibly the future state of play.
Some 40s are fitted with glass screens. There is a different mind setup between glass and traditional cockpits so you may wish to think about that aspect if you intend to fly a traditional cockpit after your PPL or NPL.
There are some operating differences between a 40 and the more typical Cessnas and Pipers most of which stem from the use of a diesel engine in the 40s. The differences are relatively small but if you were to fly a Piper or Cessna in due course you would find an hour or two might be necessary to become comfortable with these differences.
All that said the 40 handles much like any of the common training aircraft and is a good enough for the purpose for which it was designed.