If you look at the rate the SS increases each year, it continues at 7% per year until you are 70. The other factor is that the point that you reach your full retirement benefit use to be 65, but that was changed and is according to your birth year. Mine is 66 years and 2 months, and I just started SS, I did not need the income in previous years because I continued to do medical consulting and was able to keep our head above water through the years. You can easily sign up on-line or schedule and appointment if you want to do it live. I signed up last month and did it on-line, I did Medicare the previous year.
The biggest issue with retiring before you are 65 is medical insurance and the high deductibles, my medical insurance premium before I turned 65 was $1300+ a month (Platinum plan and you still had a 6K deductible). So the insurance costs is killer until you hit 65, and then I recommend standard Medicare plus a supplemental. Medicare Advantage should be called Medicare disadvantage, your monthly cost may be less but Medicare sells you to other insurance carriers and they decide what they are going to pay for and what they are not (it has nothing to do with what Medicare covers), same for drugs. We had friends who signed up for it, he had to have a cardiac ablative therapy for and arrhythmia and his plan did not cover it. In addition they do not cover you out of state/traveling. To screw you even further, if you decide to leave Medicare Advantage to go to regular Medicare, any supplemental insurer can refuse to take you or deny any per-existing medical conditions. So be forewarned, DO NOT TAKE MEDICARE ADVANTAGE, to save a few bucks, I guarantee you will regret it if you need medical care.
As far as SS and when to take it, well you can run the calculations as to taking it earlier and the break even point, if I recall it is something like 10-12 years you would make up the difference. Remember that SS was never meant to be a full retirement income, and should only represent something like 40-60% of your retirement income if possible. The problem these days is pensions are becoming a thing of the past, 401/403/IRA's make diddly squat and the stock market is a total crap shoot and can you weather a drop of 20-30% or more loss of your savings when the market takes a crap. Ideally one has several sources of income and can get through some rough spots if one pot is not making a profit. Heck you can have a pot full of money in the bank and get 0.04% interest from the bank, maybe 0.4% in a high yield account that then turn around and they offer you a credit card at 28% interest. Yep, there is something wrong in our systems.