The key here is investing the total amount of what one is ready to risk from the start rather than going gradually over time.
I accumulated bitcoins until May, this year. Now I am dishoarding.
I think if you start now, the wisest choice is to buy as much as you dare (spread it over 3-6 months, maximum, if sum is really large) and then diversify according to the plan.
Actually what matters is the number of bitcoins. Those with 1-digit number of them are rich, 2 digits are super rich, 3 digits are hyper rich and 4 digits are ultra rich when 1 bitcoin is equivalent to millions of today's dollars.
An alternative way to this savings plan is just to buy a required number of bitcoins and put it into a paper wallet. But this is not so good because the value involved is so high that you better start preparing your new life already. It can be achieved with periodical dividends from the bitcoin stash, which gradually get bigger and enable you to upgrade your standard of living, etc. gradually.
Whether you are free or not is really not about money. I fully believe that 1 bitcoin is enough freedom what comes to money, if bitcoin truly takes off. There will mathematically never be more than 2 million holders of 1 bitcoin. (See
this for discussion.) For comparison: there are
29 million dollar millionaires in the world now.