Consider the original plan for the war by the Central Powers: the main part of the war would be Germany and Austria-Hungary against Russia. To stop the western nations of the Entente (i.e., Britain and France) from turning this into a two front war (three front, if you include Austria-Hungary vs Serbia), France and Britain would be knocked out of the war with a lightning offensive before Russia could mobilise.

This didn't work. When this was obvious to the Germans, they entrenched in the best available defensive positions on the Western Front, and settled down for the war in the east. The war had become the feared two front war.

While Russia had a large army, it was short of weapons and munitions. It was in the Central Powers' best interests to keep it that way. Stopping Britain and France from supplying Russia was important. What were the routes for supply? The Baltic was blocked by the German navy. The Trans-Siberian railway wasn't complete yet, so Vladivostok was out of the picture (it was completed in 1915, but even then, capacity was limited). The Arctic route froze in winter (Murmansk was ice-free, but the Murmask Railway was only completed in 1917 - it was a wartime project to make an ice-free Arctic port (Murmansk) available). The only good route was the Black Sea.

The Black Sea route was available while the Ottomans were neutral. With their entry into the war alongside the Central Powers, Russia's problems multiplied: their main supply route from Britain and France was blocked, and a Caucasian front opened up. It was in the best interests of Britain and France to knock the Ottomans out of the war, and re-open the Black Sea route to Russia. Their armies were busy along the Western Front, so a naval operation was attempted. The idea was simple: sail a battle fleet into the Sea of Marmara, stand off Istanbul, and shell it until the Ottomans surrendered. The problem was that the Dardanelles were mined, and the minefields protected by artillery. Battleships and minesweepers would have to work together, with the battleships and cruisers (and landings by marines) taking out the artillery, and the minesweepers clearing the mines.

It didn't work. Thus, the idea of a major landing on the Gallipoli Peninsula, to allow the artillery covered the minefields to be eliminated from the landward side (at least on the northern side of the Dardanelles).

The main motive was to keep Russia in the war, and as well-supplied as possible to reduce German pressure on the Western Front.

For some reading suggestions, you could consider one of two books by Harvey Broadbent, which cover the Ottoman side of the picture:

• the more popular history one: Defending Gallipoli: The Turkish Story, https://www.mup.com.au/books/defending-gallipoli-paperback-softback

• more detailed and more academic: Gallipoli, the Turkish Defence: The Story from the Turkish documents, https://www.mup.com.au/books/gallipoli-the-turkish-defence-hardback

I don't have a particular British/French-oriented book to recommend.