Answer
Bhakti is of two types: one is polytheistic bhakti, i.e., devotion to multiple deities simultaneously. But in the Gita, the Lord's recommendation is different. The sole scripture of Bhagavad Dharma is the Gita, which is the direct speech of Ishvara. For this reason, all religious texts composed by human beings are valid only insofar as they do not contradict the Lord's own words.
The Lord has clearly stated in the Gita that worship of the devatas quickly fulfills your material desires. Bhagavan Shiva is a devata — indeed, a Mahadevata (great deity). Therefore, those devotees who practice bhakti solely for the fulfillment of their desires can simultaneously worship Shiva, Shakti, Ganesha, Krishna — all of them. And as occasions arise, they may beseech these devatas for the fulfillment of their wishes. However, such people can never attain moksha; they may gain svarga through meritorious deeds, but never liberation.
For moksha, one must practice "ananya bhakti" (exclusive devotion) to Ishvara — that is, devotion to no other, only to the One.
By practicing ananya bhakti to Ishvara, the devotee does not even need to separately ask for the fulfillment of desires — Ishvara Himself fulfills those desires that are appropriate for the devotee and do not become obstacles on the path to moksha. And truthfully, desires are the root of suffering. Following the Bhagavad Gita will gradually destroy all your worldly desires. And only then will divine bliss (divyananda) arise.
The devatas do not look after your long-term interest. They too cannot and do not fulfill every desire of yours — everyone must have experienced this. Occasionally, some desire may get fulfilled, but there is no guarantee.
Therefore, if you wish to live like an ordinary person and continue revolving in this cycle of birth and death by taking birth again and again, then there is no harm in worshipping various deities. Worship Mahadeva as well as Shri Krishna. If the occasion arises, worship Durga ji and Hanuman ji too. And generally, this is exactly what most people do.
But if your goal is to be free from suffering forever and you desire divine happiness even in this life, then you should worship one Ishvara alone — only and exclusively the One.
You may show respect to other devatas, offer them pranama, but never make any petition to them — never. If you must petition, petition only your chosen Ishvara.
Do not cultivate excessive closeness with the devatas — ever. This is somewhat analogous to how a virtuous person remains devoted solely to their spouse, even though at the office they interact with many women in an official capacity. But cultivating intimacy with those women would be improper. It is considered "adultery." Similarly, cultivating closeness with any devata constitutes "spiritual adultery." The Lord repeatedly speaks of "avyabhicharini" (unwavering, exclusive) bhakti in the Gita.
Now, if you must choose only one, my counsel is to choose Laddu Gopal. There are several reasons for this. First, worship of the one you love will accelerate your spiritual progress and bring greater joy — and joy is a primary goal of life. Second, all the shastras collectively establish that sattva guna is superior to rajo guna and tamo guna. Brahma is a rajoguni devata and Shiva is a tamoguni devata.
Therefore, whether you choose by reason or by feeling, in my view, choosing Laddu Gopal is the right choice for you.
You can change your chosen deity. Bhagavan Shiva's own object of worship is Bhagavan Vishnu Himself — the Shiva Purana itself states this. Therefore, if you begin worshipping Bhagavan Vishnu, i.e., Bhagavan Krishna, in place of Bhagavan Shiva, Bhagavan Shiva will feel no distress whatsoever — only joy.
If you read the Shiva Purana, even though it is a text of the Shaiva tradition, it too records that when Bhagavan Rama was wandering in the forest, enacting the lila of grief over Bhagavati Sita, Bhagavan Shiva beheld Him there and experienced wondrous bliss, offered Him pranama. And Sati then realized that Rama is verily an avatara of Vishnu — that is why Bhagavan Shiva had offered Him pranama and bowed His head. And when Mata Sati tested Bhagavan Rama by assuming the form of Mata Sita, Shiva mentally renounced Sati, and ultimately Sati had to immolate herself in the fire of yoga and assume a new body.
This story was not invented by Tulsidas; Tulsidas took it from the Shiva Purana itself. Shri Krishna too is an avatara of Bhagavan Vishnu.
Moreover, the element of ananda (bliss) is so manifest in Bhagavan Krishna that it is impossible for His devotees to remain without joy. His lilas contain infinite bliss. Therefore, with firm resolve and without any inner conflict, make Him alone your chosen deity.
If you practice bhakti with inner conflict (dvandva), you will not receive the full fruit of bhakti. Nor will you experience full bliss, because dvandva destroys bliss.
If you require scriptural evidence on this matter, that too can be provided in detail.