Rust is correct, the TMB does not require a down payment.
Past versions of Traveller required 20% down and financing of the remaining.
Ship Shares reduce the price of the ship. Either 1 MCr or 1% of the price is reduced per ship share (depending on how you read the rules, there are conflicts).
Personally, I require 20% down and Ship Shares may be used to either pay part of the downpayment or to reduce ship price (Player's Choice).
Whether payments are due at the first or end of the month is up to the Referee. Personally, I think it would vary by world or bank.
Hope that helps.