False.
The Commission election involves several steps.
First, the President is nominated. While this is technically a power of the European Council (not to be confused with the Council of the European Union), in 2004 the Parliament won the right to determine the president and the nomination by the European Council is only a formality. (Similar to the appointment of the British PM by the British monarch).
In practice, the choice of president is now the result of the elections to the European Parliament through the so-called "spitzenkandidaten" process [1], where each group in the EP nominates a candidate and the candidate of the largest party that can command a majority in the EP is chosen, who is then formally appointed.
Second, the Commission President in conjunction with the member states nominates the remaining commissioners. The EP conducts hearings, after which the Commission is voted on. The EP can reject the Commission. In 2014, this resulted in the rejection of the Slovenian commissioner [2] and the Hungarian commissioner being stripped of the citizenship portfolio [3] as the result of questions regarding Hungary's human rights record.
The EP can also remove the Commission through a motion of censure, Article 234 TFEU. This is what happened to the Santer commission (except that they resigned before the EP could vote them out of office).
Note that under the British system, the Prime Minister and his or her cabinet does not even have to face hearings. The members of the cabinet are simply chosen by the PM, the PM is appointed by the monarch.
That only the Commission can initiate legislation is not much of an issue and has more to do with how complex EU legislation is, which has to conform to the legislation of all the member states. The EP can propose legislation through Article 225 TFEU, can attach legislation to other legislation (such as the budget) through amendments if necessary (similar to how the US Senate gets around the Origination Clause) and simply force the Commission to initiate legislation or block other legislation (or, in the worst case, vote the Commission out of office).
[1] https://en.wikipedia.org/wiki/President_of_the_European_Comm...
[2] http://www.irishtimes.com/news/world/europe/slovenia-s-nomin...
[3] http://www.novinite.com/articles/164253/Hungary's+Navracsics...