Retirement & SS windfall

I retired this year at 60 receiving only my pension check while paying a portion of medical until I reach 65.  I have enough credits to collect SS, but I’m under the windfall, since I  worked in a company for my last 30 that didn’t pay into SS so when I start collecting I will not collect my full Social Security.  Should I collect my Social Security at 62 versus waiting till 65-67?  When I start collecting Social Security will that put me in a higher tax bracket?  What  can I do so I’m not surprised at the end of the year when I go to file my taxes?  Should I ask that additional money be taken from my federal and state taxes and if so how much so I’m not surprised having to pay a huge tax payment.  Thank you