Switch to skill work visa

[pinki]

Hi Team
I am planning to switch from my Tier 2 General visa to Skilled worker visa. .I have to provide the start date for my visa .I need some advise on this .There are two Strat dates options provided by my sponsor company ( 17 Jan 2022 or 07 Feb 2022) .I have to choose one of them .I have seen many people wait for there visa decision before they put the paper to current company .I felt it's good for 1 or 2 month notice period but might not practical for 3 month notice period. Can anyone give some advise on this ?
Which start date should i give to future employer ?
When to put the resignation in my current company ? should i wait for visa decision then it may conflict with the Start date .
If i give the priorty visa , it may not work due to current backlog with the home office .
Please suggest

Current visa expiry date -07/2024 .
Current Notice Period - 3 months