I am interested in buying around $100k of Bitcoin.

Is the best way to buy in small quantities on an exchange?

I read that some banks won't let you transfer money to a BTC exchange, and worse, may close your account.

I worry that the exchange may fail and I would lose all my Bitcoin

I worry that Bitcoins anonymity is not going to work, after all, my bank will know that I transferred funds to a particular BTC exchange, or to a block chain account.

I worry that if I manage to get money into Bitcoin, I may have trouble getting it back due to financial regulations.

I worry that I will lose my Bitcoin wallet due to an Internet problem.

I worry that my Bitcoin will be lost if I die.

By the way I have no worries about price changes.  I can take the financial loss if there is one.

Please tell me if there are solutions to these problems.