The latest schedule from Sharjah to Bandar Abbas is on Sun - Tues at 22:00. The ferries go back from Bandar Abbas to Sharjah on Mon and Wed. The latest cost is 150$ for first class and 140$ economy (round trip).
They are all operated by Iranian ship company Valfajr and tickets are sold both by the company and its representatives.
By the way, (Another routes is available from Dubai to Bandar Lengeh but it is not recommended as it is off-route for tourists).
Bandar Abbas is preferable, cuz it is a big city with places to visit and nice hotels to stay in overnight. Frequent connections are available. From Bandar Abbas, you can easily take the bus to Shiraz, Kerman or Tehran. Alternatively, take the train to Kerman or fly to Shiraz or any other major city.
To book a ticket visit Iran Travel Ferry service and fill in the booking form.