So with respect to the travel date in the application, would there be an issue if I put something 2-3 weeks from the date of the application? Ideally, if the visa does get processed in 2-3 weeks, then I would like to obviously fly into the UK as soon as the visa is approved.
Yes, that's fine - if the visa isn't issued in time for that date, it will just be made valid from the date they do issue it.
Or does the government expect that we put our tentative travel date to be 12 weeks out from the time of the application to allow for the max processing time?...What if the visa gets approved earlier than the travel date in the application - can one then travel or would one have to wait until the travel date noted in the application/visa?....
No, you wouldn't be able to travel until the start date on the visa, which will be the travel date you put on the application... because it won't be valid for travel until that date.
Which is exactly why you should not put a date 12 weeks out if you aren't willing to wait that long!
It used to be that Sheffield were a bit lax with making the visa valid from your travel date and would sometimes make it valid from the date of issue, regardless of the date you put... but that was when the visa sticker was valid for 33 months and you had 3 months and 28 days from the valid date to enter the UK and still qualify for future visas in time.
However, now that the visa sticker is only valid for 30 days, they have been sticking to the travel date you put because there is less leeway to enter the UK - so if you put a date 12 weeks ahead and then the visa is issued in 3 days, you'll still have to wait another 11.5 weeks before you can travel!