General answer: Wehrmacht didn't "choose". It was forced to do so by political leadership (Hitler really wanted to take it) and by the Red Army (stubbornly refused to give it up).
In general, battle story resembles that of Stalingrad:
If it's "storming vs siege" question:
Wehrmacht tried to storm it, but then Hitler decided (see [1]) to starve it and bombard into submission. Per Generalplan "Ost", city must be flooded, population - starved.
1941, July 19–23: First attack on Leningrad by Army Group North is stopped 100 km south of the city (Luga line)
1941, August 15: Luga line broken thru
1941, September 19: German troops are stopped 10 km from Leningrad, railroad station at Mga taken
1942, April 4: Operation "Eis Stoß" (Ice impact) - intensive Luftwaffe bombardment of ships and city infrastucture
1942, June–September: Newer heavy artillery is stationed 10–28 km from the city and bombards Leningrad with 800 kg shells.
from Nuremberg protocols, day 65 (22 Feb. 46), Raginsky's address to court:
The first document is a secret directive of the Naval Staff, numbered Ia 1601/41, dated 22 September, 1941. It is entitled "The Future of the City of Petersburg". This document has already been presented by our American colleagues. Therefore, while we are also in possession of the original of this document, which was distributed in several copies, I believe that it does not have to be read into the record. With your permission, Mr. President, I shall remind the Tribunal of the contents of this directive. In this directive it is stated: "The Fuehrer has decided to wipe the city of Petersburg from the face of the earth"; that it is planned to blockade the city securely, to subject it to artillery bombardment of all calibres and by means of constant bombing from the air to raze the city to the ground. It is also decreed in the order that should there be a request for capitulation, such a request should be turned down by the Germans. Finally, it is stated in this document that this directive emanates not only from the Naval Staff, but also from the O.K.W.
...
The second document, bearing the number Document C-123, presented to the Court as Exhibit Number USSR-114, is also a top secret order of the Supreme Command of the Armed Forces, dated 7 October 1941, Number 44/1675/41, and signed by the Defendant Jodl. This document, Your Honors, is to be found on Pages 69 and 70 in the document book. I read into the record the text of this document, or rather a few excerpts from this letter on Page 14 of my presentation. I read the first paragraph of the letter:
"The Fuehrer has again decided that a capitulation of Leningrad or, later, of Moscow is not to be accepted even if it is offered by the enemy."
And further the last but one paragraph of this page:
"Therefore, no German soldier is to enter these cities. By our fire we must force all who try to leave the city through our lines to turn back. The exodus of the population through the smaller, unguarded gaps toward the interior of Russia is only to be welcomed. Before the cities are taken, they are to be weakened by artillery fire and air attacks, and their population should be caused to flee.
"We cannot take the responsibility of endangering our soldiers' lives in order to save Russian cities from fire, nor that of feeding the population of these cities at the expense of the German homeland....
"All commanding officers shall be informed of this will of the Fuehrer."
If it's a question "why to bother taking it at all"?
Leningrad is highly symbolic to all russian people ("2nd capital", "northern capital", "intellectual capital" etc.), with special meaning attached by communist leadership ("cradle of Revolution", "Lenin's city" etc.)
Hitler really wanted to take it. Generalplan "Ost" envisioned that city will be flooded, so no trace of "Bolshevism birtplace" will remain. On Sep 22, 1941: Hitler issues "Directive No. 1601" ordering "St. Petersburg must be erased from the face of the Earth" and "we have no interest in saving lives of civilian population."
high-value industrial hub. It produced tanks KV, SMGs - to name a few.
strategically placed. Were it to fall, a lot of Wehrmacht forces will be freed to join assault on Moscow.
It is debatable (from purely military prospective) whether more optimal course of action for Wehrmacht would be to leave a blocking force and concentrate on Moscow. Some of that happened in 1942-1943, but in 1941 Army Group North was quite strong and capable of storming the city.
Sources
Map - Assault of Leningrad, 1-30 Aug 1941. Arrows depicts push of Wehrmacht toward the city and encirclement.
Russian, PDF - Krinov Y. S. Luga Line. Year of 1941 = Кринов Ю. С. Лужский рубеж. Год 1941-й.. See page 17 - detailed moves of Finn and Wehrmacht forces, July-Sep 1941.
German - Czeslaw Madajczyk. Generalplan "Ost". Documents = Czeslaw Madajczyk. Vom Generalplan Ost Zum Generalsiedlungsplan: Dokumente . In german, but there is an article by Madajczyk with analysis in English.
David M. Glantz. Siege of Leningrad, 1941-1944: 900 Days of Terror
